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For a wall mounted shelf to isolate feedback the wall needs to be a structural wall or load bearing wall, otherwise the wall moves with the floor.

Other feedback issues, assuming the turntable is set up correctly, could be in room base response. Locate the shelf away from corners, and away from between the speakers - these areas generally have high base nodes.

Also check your set up, tracking force and antiscate, make sure the arm is mounted tightly - not loose. Check bearing and turntable feet are not loose. Make sure there are no rattles in the shelf itself.

A common problem exacerbated by your relatively light weight turntable. Mass being one of the easier ways of controlling vibration. It simply takes a lot more energy to move a large mass than a small one.  

Okay so you need more mass. The classic cheap solution is sand, mixed with a little mineral oil to keep the dust down, in a box. The more sand the more mass and the better it works but as little as an inch or two makes a huge improvement and costs next to nothing.  

If you don't like that one no problem, next up the food chain in cost and performance, Nobsound springs. These are crazy good for the money but I know people with light turntables need to add mass to make springs work properly. What you want are springs soft enough the load compresses them a lot, at least half way, and when moved the load oscillates very slowly, no more than 2 or 3Hz. Think the way a Linn bounces. 

At the top of the pyramid are Townshend Pods. These things are absolutely awesome. Not only under turntables, its surprising how well they work under amps, especially tube amps. If your table is under 15 lbs you may need to add some mass with a board or sand box but it will be worth it. Not only will your feedback be eliminated the sound will be better than you ever heard it on concrete. 

All these vibrations are coming from the subs, through the floor and walls, to your system. Nobsound springs under the subs will be a huge improvement. If it was me, I would do Nobsound under all the speakers, and CD, and use Pods under the more critical turntable and amp. That's what I do - all of it including the sand boxes - and it works great.  https://systems.audiogon.com/systems/8367 

Pods probably seem like overkill in your system. They are expensive, no doubt. You can save a lot with sand and Nobsound. Its hard to believe how well springs work until you try them. That's what I did, and its why I always recommend a gradual incremental type approach like this.

You cold put a hundred cinder blocks under that turntable and it would not help. Your only hope in this situation will be a subsonic filter. I doubt you will cough up for a MinusK platform. This is why suspended turntables like the Sota are so important. You can kiss this stuff goodbye. 
Any wall in the house is going to vibrate to some extent. Wall shelfs might help against footfalls but not to feedback. 
The best subsonic filters are digital as they can roll of much faster without affecting the audio band. 
It is possible that a cartridge that is less compliant with a lower output might help but I would not guarantee that. There may be a less expensive isolation platform that will work but I do not know any. Any isolation feet or platform would have to be sprung to have a resonance frequency around 2 Hz.  

Try to isolate the subs on their own base that decouples them from the floor to remove the floor excitement they are creating. A good way to do this is to use a slab of stone under the subs. It is effective and relatively cheap and painless to implement.

Can you be more specific? What do you mean “vibration”? Is the sub output vibrating/energizing the room enough to effect the TT during playback, or are you getting woofer subsonics when the stylus hits the vinyl? Two different problems. 

Try plug the ports of subwoofer?

Your Rega wall support is made from hollow metal that can resonate. Putting P3 directly on it will not help alone. You need to decouple somehow your tt from the shelf. And still airborne vibrations would affect its lightweight chassis. Try to have the lid removed when listening.
G

Wall mounts generally don't work all that well. To isolate a turntable from low frequencies you need a **non-resonant** mass beneath the turntable; to which the turntable is coupled with points.

You use points to couple, so as to allow vibration to move from one object to another (where hopefully it is damped). You use squishies to isolate, to prevent vibration from moving from one object to another. So you don't use squishies between a turntable and platform because airborne vibration occurring in the turntable isn't treated.


If the platform is in a stand, it should be isolated from the stand by squishies, like these:
https://www.isolateit.com/hemispheres.html
The stand will sit on the floor of course but if you can mount it on a set of bearings the turntable will be more unassailable and also more impervious to foot falls. These will work although you might have to do a bit of fiddling:

https://www.symposiumusa.com/rbjr.html
Good Luck.

@ lenmc2964;
Let’s get down to basics-to the very root of the problem-subwoofers and turntables do not play nicely with each other. You need to have a very large room or better yet, put the turntable in a different room. Most people don’t want to do that for the obvious reasons of inconvenience, long runs of IC’s, etc.
My advice is as simple as the problem; maintain the subs when using your CDP and disengage the subs when playing vinyl. In your case, a Rega 3 is never going to plumb the depths of bass anyway. But even if you had a 50K turntable rig, subs are going to adversely affect the sound.
I am in the camp that believes that the beauty of vinyl lies in touch, texture, and tone. Sure, folks with Mikey Fremer money and taste can achieve deep bass but it comes at a huge price and you don’t need it to enjoy music. I am not familiar with your loudspeakers but I have a smallish 15x13x8 dedicated listening room that opens into an adjoining room with 150 tube watts driving DeVore O/93’s and I get very satisfying bass even though it drops off at 40hz or so. Having heavy duty Symposium racks (3) for my equipment and each of my two vintage idlers with Reed 3P arms helps. Sometimes I swap out the DeVores for Spendor D7.2’s and the bass is even more limited but they give the impression of very solid bass. I have an LCD Soundsystem record that awes friends and visitors with startling bass slam and dynamics.
IMHO the only reason for subs is home theater or if you are into industrial/synth/techo type music.
Granted, there are those that disagree with this view-like Jim Smith of all people-and I have nothing but respect for him-having told me that properly placed subs adds life and realism to the male voice-that Johnny Cash’s voice becomes much more real and satisfying with subs. Perhaps. But Jim Smith also told me he is a digital-only kind of guy.

I have a very heavy TT--Lenco w/ Pete Riggle Woody arm.  I get no howling or feedback when playing records.  The TT weighs about 115 lbs. and sits on a Star Sound Sistrum rack's points.  There are 2 other components that are on shelves on that rack also.  I have 2 sets of racks so they are much lower than a tall one.  Mine used to be 4 ft. tall but I had Star Sound cut the support rods so they are about 1/2 as tall and a even more stable.

Bob

Some strange opinions here. Atma-Sphere makes the most sense. No, subs and turntables do not play well together but it is imminently possible to make it work. I use a very powerful subwoofer array and I have ZERO difficulty playing the turntable at 105 dB. I use a suspended turntable resonating at 2 dB and an 80 dB/oct digital subsonic filter down 3 dB at 18 Hz. A well isolated turntable set up correctly will do tolerably well without a subsonic filter depending on how loud you go. I have not tried the situation with a table like the Rega and just a subsonic filter but, if the cartridge is chosen to give a tonearm resonance frequency of 8-10 Hz it should be OK. A turntable has to be isolated to work at the highest level of performance unless you put the turntable in another room which some people do. I actually boost the bass. Without a subsonic filter my woofers would be dancing the jig but, with the filter they are perfectly quiet until a low note comes along. Unfortunately analog filters do not work well. Yuo can't roll them off fast enough and they create issues with the bass which is why audiophiles hate them. The situation is totally different with digital filters. Yes, I digitize my turntable. It is converted t 24/192 by a Benchmark ADC 1. The transfer and back is totally invisible an opinion also relayed by Michael Fremer who uses the same digital set up I do.
Our OP needs to put his turntable in another room, get a subsonic filter or get a suspended turntable. You can suspend the Rega with several options on the market but, if the system does not have a very low resonance frequency, below 3 Hz, it will not work. The first hint that you might be on to something is isolators that are "sized" to the weight of the turntable. 

OP, I went through a similar issue with my old turntable, and I think what helped the most was a pair of subsonic high pass filters. I found a pair on Amazon pretty inexpensively, and they worked, search for : Harrison Labs FMOD Inline Crossover Pair 20 Hz High Pass RCA. About $30 for the pair, so worth checking out. 20Hz isn’t so bad, and solved my problem once installed. In addition, yes, I put my table in a tray of sand, got a decent record clamp, provided bracing/support to the floor in the basement, etc etc. But the high pass filter was, I believe, the key solution.

But

The best solution was my ‘new’ SOTA Sapphire table. No filters, no sand, and don’t even need a record clamp. All the issues I had before, the SOTA solved. Nothing phases it; Vibration-wise or sonically via any feedback. ‘Quiet as a church mouse’ and no additional tricks or tweaks necessary.

Thank you for all the input and advice. I’m going to try the springs under the subs and I ordered a isolation platform from maple shade. Will try the RP3 on it with springs under the turntable. Once again thank you all. 

Update as of right now I’m rumble free. Fingers crossed. I did get the springs and put them under the sub’s then took the turntable off the wall removed the feet and put three 2" Dia Sorbothane Hemisphere feet in there place. Also put four Herbie’s fat dots under the phono pre amp. I want to say thank you to everyone who helped. Now I can start fine tuning my system. Have not received the Maple Shade platform but will put the RP 3 on it when it gets here. One more layer can’t hurt.