Best turntable under $2000

 Your areas of dissatisfaction with your Rega P2 turntable suggest to me that you would be happier with a direct drive turntable. The faults that you cite in respect of the Rega are possibly due to speed inaccuracy that is endemic with belt drive turntables, like the rega, and like the VPI turntables. What happens as you spend more money is hopefully that this problem Is more and more successfully addressed with more expensive belt drive turntables. However, I think you might like the sound of direct drive turntables, and there are some that you could purchase for less money. There are many VPI adherents contributing to this thread, and they are likely to disagree with my sentiments. They are entitled to their opinions. And certainly VPI is a step up from rega in the lower cost and midprice category.

I have been extremely pleased with my Clearaudio Concept Wood MC. You should be able to get one used for under $2K. I have it paired to an iPhono II phono preamp. Pretty amazing sound for the money. 

1200gr

To respond to the preference for VPI, I have a VPI Aries 2 and it is a great table and with a Lyra Delos outclasses any sub $2000 turntable. But, as I recall, I paid close to $4000 for that table with JMW 10.5 arm. I also previously owned an original VPI Traveler, but IMO the 1200GR sounds superior to the Traveler. It is a superb deck for $1700 and my audio/music listening friends agree.

If you want a turntable for dummies (like the book series :) get a Rega with a Rega cartridge.  No setup required and the sound will be good but not nearly as good as it could be for the $,  
If you have some moderate capability to mount and align a cartridge then the GR would be difficult to beat.  A 1200GR with Nagaoka MP 500 for example will shred the sound of the P6 with Ania cartridge.  
The GR will give you a speed precise energetic, neutral sound.  
VPIs offer a lush, high mass belt drive sound that I have found to be overly warm and sluggish, along with lots of alignment skills required.