Upgrade cartridge or turntable?

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.

As a frustrated and another former  Rega RP3 owner, I would unabashedly recommend a different turntable.  Aside from any isolation issues, the lack of an easy VTA adjustment for different cartridges is just plain arrogant.  Some <$600 turntables have a VTA adjustment process with simple set screws at the base. Some carts will not even mount due to their own height.  

There are tons of <$2000 tables out there Rega.  BTW, the Ortofon 2M Blue is quite good IMO, but the market for REALLY good, fairly inexpensive moving coil cartridges has expanded rapidly in the past few years.  

Get a new stylus and save more money. Let us know when you get to $5000.

I'd throw a Dynavector 20 XL or whatever suits your budget on the table - the Planar 4 can definitely handle a big cartridge upgrade no problem.