speaking as former Rega P3 owner I don't think you're going to recognize a transformational step change via cart replacement alone. I'd consider applying your $2000 TT budget toward an upgrade on the used market. The P3's inability to provide really solid isolation is going to prevent you from fully recognizing the benefits from any cart upgrade IMO.
Upgrade cartridge or turntable?
I have a Rega Planar 3 turntable with an Ortofon Blue cartridge which has served me well. I’ve had them both now for two years and am around the 1000 hr mark which in itself draws debate. I’m looking for opinions on either a cartridge upgrade, or a turntable. Can go to 2000 for TT, also considering MC cartridge which would involve a new phonostage. Let’s hear it.