That would be a step sideways to go for the RP3 instead of the MMF 5. While the Rega do have the better tone arm (the new Rega RB303) the Pro-Ject 9 tone arm in the Music Hall is still good (Linn uses the same tone arm in their much more expensive Linn LP12 Majik package), and the Music Hall has a more advanced plinth construction with the split-plinth that means that the motor is on one plinth and the tone arm and platter on the other so the motor is better isolated on the Music Hall.
While the Rega RP3 is a highly musical turntable (as all offerings from Rega, sort of budget Linn), you may get a different sound more than a real improvement or upgrade. No, I agree with the other posters here that you should check the cartridge and turntable setup. It shouldn't sound muddy. You could also try a different cartridge, even if I do feel that the Goldring 1042 is actually quite a good one not exactly lacking in precision. But if you want something crisper then Goldring 2100 or 2200, or Ortofon 2M Blue are good choices.