If the Rega can't be fitted on its wall shelf, and the motor is suspended rather than the later fixed version (now in 24V guise), I'd probably flog it and look for a modern replacement - apparently a new Planar 2 will outperform an old Planar 3/RB300 as everything's been refined and the arm is claimed to be better anyway. Trouble is, 'proper' decks really start at a grand and go higher these days
Not everyone will find this, but my thoughts on the old RB arms is that it's so easy to get them to sound musically bland and rather 'muted' in tone and 'feel.' Metal armboards aren't always best ime with these arms and possibly a techie with one of speedy-Steve's wooden jobbies may be better.
Finally, you're stuck with a 10XV - now very silly money to buy new and rather too 'safe' sounding for me, like a DL110 which it really competes with in my experience and used to when they basically cost the same when the V was an almost identical IV - only the mounting plate was altered I was told and this to re-negotiate manufacturing and hence retail prices... Not sure your existing deck wouldn't sound far better with an AT-F7 as the previous F5 worked so brilliantly in an RB300, one taming the other so well I thought. The F7 will need an MC input though.
Such a shame the sub £1k turntable market is stuck with the same old options. A stock techie is different but maybe not really 'better' than a modern Rega 3, but you may find that one excels where the other lags - the *modern* Rega perhaps, has the better arm and tonal/musical setup, but the Techie has proper pitch stability and runs at precisely the right speed while adding a certain sense of 'drive' to the sound...
Good luck. May be a good idea to save harder and change the entire thing for the next level up? In the meantime, tighten the tonearm fixing nut carefully as well as the main bearing nut, replace the mat if it's old and going fluffy and probably belt too if it's had a thousand or so hours of use. These decks really sound best on their wall bracket, as the bass is so much better I always thought.
Tear down these walls; Cut the ties that held me
Crying out at the top of my voice; Tell me now if you can hear me