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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.