The Rega RP3 is a terrible turntable, I know that since I bought one 7-8 years ago. Tried a lot of cartrtidges from the Goldring 1042, Sumiko Blue Point Special Evo 2 and Dynavector 10x5, etc. It was so bad it almost made me quit analog for good. Everything was sounding thin, without body and musical involvement. The RP3's tonearm and the cartridges were perfectly aligned, I had the Rega TT-PSU power supply upgrade as well, it did nothing for me.
Switched to a Michell Gyrodec, the groove and musical excitement came back. A lot of upgrade potential with the power supplies, choice of tonearms, platter/clamp/suspension upgrades, etc. I also hear the entry level Dr. Feickert is a terrific sounding TT as well.
But my suggestion, the RP3 should go, it's just a waste of time, money and space.