Turntable and Arm Combination in 5K range (maximum)

Look for Reed 3p, it's available in '9.5 , '10.5 or '12 inch with various armtubes to match with your TeKaitora cartridge. This is one of the best tonearm on the market today, fully adjustable (azimuth and vta on the fly). 

I'd be inclined to look at a non-belt drive table if I was listening to piano.

Denon DP-80 in original or custom made plinth.
more info here

...add Reed 3p tonearm and you're done

Get a SOTA Sapphire and put your Origin live tonearm on it. SOTA will install it for your. Call and talk to Donna 608 538 3500

If you're open to used, it doesn't get much better than this.
https://www.audiogon.com/listings/lisa0e5i-vpi-hr-x-turntables

It even comes with a great cart. This seller is offering a good deal. Ignore any VPI bashing.

For added speed accuracy, use your $1200 stimulus check for the ADS
https://www.audiogon.com/listings/lisa13a7-vpi-sds-synchronous-drive-system-excellent-upgrade-for-any-vpi-table-ac-conditioners  

Assuming you have a phono stage up to the task, you will have a VERY nice setup for minimum expense.

Also be aware those prices are NEGOTIABLE. You may be able to score them for LE$$.

Excellent time to buy pricey gear.

Thanks to all of you for your suggestions, certainly open to more but I will pursue some of these.  The Reed tonearm looks really nice but above my budget unless discounts and/or package dials are available..  Denon DP-80 reference didn't get me much except to a forum with little activity.  Don't know what to think of the HRX, it does seem like a decent deal.  I located another with the rim drive option, but it is higher.  That is a very LARGE table.  How would the arm mate with my TKR?  MijoStyn2, who will answer when I call the number you gave me, re: the Sota?

For piano music a direct drive turntable like the Technics 1200G would be something to consider.  The sound is certainly quick and dynamic!

How are the arms on the Technics?

Is your OL Illustrious tonearm a recent MK3C?  Properly set up I was able to use mine with excellent results on a OL Resolution mk3-2 with their speed control (LSC) upgrade.  I used a Ortofon Windfeld Ti, Kiseki Purpleheart, and Koetsu Rosewood Signature Platinum. The arm is now moved to a dual arm OL Sovereign paired with the Enterprise C arm. Your arm takes a little attention to detail, as all do, to perform at a high level but you may be shortchanging yourself expecting to better its performance as well as acquiring a different TT in the price range you are targeting.  

Thanks to all of you for your suggestions, certainly open to more but I will pursue some of these. The Reed tonearm looks really nice but above my budget unless discounts and/or package dials are available..

I bought my Reed 3p "12 as a demo from the manufacturer, you could look for demo unit from the official dealers or simply on used market, it will save you a lot.

Denon DP-80 reference didn’t get me much except to a forum with little activity.

This is one of the best vintage Direct Drive turntables that luckily is not overpriced yet, tons of information here on audiogon from experienced members. In my opinion this is the one to grab quickly before it’s not too late. I bought mine after Victor TT-101, Technics SP10 mkII, Luxman PD-444 ... This Denon DP-80 is a high-end direct drive, very well engineered, highly recommended!

You will not find much even about top of the line and extremely expensive Denon DP-100, but it means absolutely nothing, because instead you will find so many information about mediocre turntables of today which does not make them any better than some unknown vintage gear.

How are the arms on the Technics?

Technics EPA-100 (and especially EPA-100 mkII) are superb for MM cartridges and for most of the mid compliance MC. They are better and more complicated than new Technics tonearms, but new are also nice.

SO you could buy new Technics SL1200G if you like new (complete system) for $4000

So far, the suggestion that rings true with me is using my existing OL Mk3 (not mk3c) on a Sota.  So, a few questions about the Sota line -- is the vacuum unit worth doing, and what about the tables above the Sapphire in the line?  And to be clear, I am really happy with my existing tonearm.

Another point that is possiby relevant to the question of vacuum:  my vinyl is in good shape, I don't play warped records, especially with a TKR.

FWIW, should probably let you know, for much less than the cost of an arm you could tweak more performance out of your existing arm than you would believe. Maybe even more than any of the arm upgrades being considered.

First thing I would do is order some fo.Q tape and TC. This special tape has piezoelectric properties that transfer vibrational energy into heat. This lowers the noise floor dramatically revealing incredible inner detail and micro dynamics that really opens the sound up with a sensation of incredible presence.

I put one strip the length of the arm tube, on the underside where I don’t have to look at it. Very hard to see. Then I put more all around and under the base and counterweight area, again basically anywhere out of sight. But when you hear how good it works you might not care! It can also go on or near the motor, plinth, under the footers, anywhere you think it might be good to control vibration.

Its a super high quality tape with a beautiful adhesive that somehow manages to stick incredibly well yet be easily removed without leaving any residue. Just fabulous stuff. If you can’t use it all on the arm and table the rest can be used on speaker frames or the phono stage, just try it and see. For $40 by the time you use both sheets you will feel like you have a whole new arm.

Then coat all the fo.Q tape with TC. This will take the tape to a whole new level of refinement and extension. By the time you have done all this the improvement will be about as much, if not more, than when I went from a Graham 2.2 to OL Conqueror. In other words you get $3k of improvement for $350.

Next after that would be Synergisitic PHT. Green Dream and Black Widow. You can use both. Others who have followed my recommendation on this are really happy. Also ECT, which work great on the tone arm base. You can see all these being used on my table here. https://systems.audiogon.com/systems/8367

Just a thought.

Thanks for these suggestions..

I am thinking of trying these PHT's.  Can you return them if you can't hear changes?

Chakster’s recommendations for vintage direct drive and reed 2a. Less options but not far behind the 3P. This is from info from someone in the industry that I trust that knows both arms well. Also the Reeds don't stand too tall and mount nicest on these low platers of the direct drives without lowering the plinth height.

sdrsdrsdr

... Reeds don't stand too tall and mount nicest on these low platers of the direct drives without lowering the plinth height.

That doesn't make any sense. If you lower the plinth, you'll be also  lowering the height of the pickup arm. (Unless you're using an outboard arm pod, which would be unusual and also have its own set of problems.)

What DD turntables are you referring to that have "low platters?"

@cleeds 

I meant to say thin platters. Most arms stand to tall for some direct drives and the arm boards must be recessed lower than the top of the plinth. This is seen often on sp10. The reed arms are able to be adjusted  lower than most other arms.