Next step up from my Rega P3

As others pointed out, you haven't fully exploited the Rega's capabilities. Both the wiring and counterweight upgrades make noticeable improvements to an RB-300 arm. I kept my modified Rega arm and used it on a Thorens TD-850, with good results. Since there are 4 or 5 elements to this -arm, table, phono pre, cartridge, sometimes phono cable - you may be better off picking one weak point to upgrade, like the phono stage. That way you will be able to identify the source of any change in sound. You might as well take your time, since as you know, from reading this forum, it will never end.

At $3K, I'd go for a new Well Tempered Amadeus. If the reviews are even half
true, it would be a step or more up from the P3 in every way.

Firebaugh has the track record, and now he's got an affordable and consistent
source for manufacturing.

I would check this WT Amadeus, too.

Yes no doubt, Buonarroti, your budget is gone.
Next is your phono stage and choice of cartridge....

I also highly recommend the Well Tempered Amadeus in your approximate price range. I first heard the Amadeus about 10 days ago at Don Better Audio in Cleveland. It significantly outperforms even the Rega P9. I also heard it A/B'd against the new Ayre table (which was very impressive) and the Spiral Groove 1, which honestly would be my first choice for another turntable setup if money were not a consideration. I felt the Amadeus was better than the Ayre, and was surprisingly close to the SG1. I have the Basis Signature 2500/Dynavector 4/Lyra Titan setup right now, and as much as I love that setup, the turntable I will be getting for my primary system will be the Amadeus. And the Amadeus, with the top of the line EMT cartridge and Auditorium 23 RCA's (the Amadeus does not come with RCA's), will "only" be 36 percent of the MSRP for my Basis et al setup. Frankly, if the Amadeus had been available when I was auditioning turntables, I would have chosen the Amadeus over the Basis et al and saved some serious money!

I strongly feel that anyone who is thinking about spending in the vicinity of $4K (or even significantly more) on a turntable should at least audition the Amadeus. It is amazing and an absolute bargain at its price point!