Maybe later try a different cartridge. Many years ago it made a big difference in the sound on an old TT I owned.
Yup - THIS
Check on some of the forums for the RP and arm that you have and follow Rega's guidelines regarding recommended mass for the Cartridge.
I originally had a B&O MMC-3 Cartridge on my AR "The Turntable".
It tracked really well and had what I thought at the time were excellent channel-separation and overall sq
Had to add a small, stick-on weight to the headshell to allow the Tonearm to handle the little bugger and the socketed adapter that came with it.
Fast-forward to about 15 years ago -
I stumbled onto the opportunity to pick-up a Shure V15-VMR Cartridge (without stylus) for a rock-bottom price.
I got a new Shure Factory-matched Stylus for it
Spent some time setting it up and was pleasantly surprised at the difference:
-Heard stuff that I had not been hearing before (and the B&O MMC series was no slouch in its day either...)
-Tracked as good / better at Significantly Less tracking force
-Audibly better performance (better to pick-out individual instruments in Classical arrangements etc)
I feel that the difference has to do BOTH with a BETTER Cart AND the fact that the tonearm used was designed to be used with a cartridge more along the size / mass of the V15-VMR
As they are no longer available (Shure out of the phono cartridge biz) if / when mine dies - I'm probably leaning to one of the mid-grade Sumiko (Blue-Point Special series) or Grado units
Plus maybe have the tonearm re-leaded with Silver cables and a set of jacks on the plinth (presently a set of cords hanging-out of the plinth somehow "factory-ganked" onto the Tonearm leads
If I really want to "Get Crazy" - I have a booklet with the Merrill (George Merrill) Mods that used to be done to older AR XA and XB units, which even today can perform SURPRISINGLY well for as often as the urge to spin some vinyl strikes me.
ALSO - AN INEXPENSIVE IDEA TO TRY:
IIRC - the Rega Planars do not have / have much of a "suspension" for the platter / tonearm.
Placing the entire TT ON TOP of something with A LOT of mass (like 50 pounds or more) and low resonance (get some stone / marble tiles and put some felt / rubber mat between some layers) can help to isolate it from vibrations (acoustical feedback):
Low-Frequency Speakers-->Room / Audio Rack-->Turntable Movement-->Cartridge Movement-->Stylus (relative) movement -->(back to speakers)
Low-Frequency Speakers-->Room / Audio Rack-->||[
Mass / Resonance Damper]||-->(LESS) Turntable Movement-->Cartridge Movement-->Stylus (relative) movement -->(back to speakers)
If an attempt like this works, and if your Audio Rack / Stand can support the extra weight - you could check with a local stone / granite counter-top dealer, and have them shape a small piece from some scraps to give you something that will look nicer / complement your setup.