Still Need Help

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.