How much does rock-solid speed stability cost?

I've been shopping for a new turntable and have found out I am very sensitive to speed variations. I listened to several belt driven tables and couldn't find one I could tolerate (Man, the P3 was bad). I thought the Nottingham Spacedeck was going to work, but after a second listen, it started to bug me also. So I had a bright idea - why don't I get an SL1200 from Crutchfield. It's supposed to be very stable. If I don't like it I can return it.

Well, crap! It's just as bad as the others. Average speed is fine, but it's sharp, then flat, then sharp ... Anything with a pure tone like piano, french horn, or flugelhorn has audible flutter. I have a hard time finding ANY recording that doesn't do this.

I guess almost 20 years of listening to nothing but CDs has ruined me. My big question to y'all is...Is this just the way analog is, and it's probably not for me? Or, can spending more money fix the problem? I only have about 200 records, most collected from mid '70s through early '80s. I really can't justify spending more than $2000 on a turntable and arm. I haven't heard the VPI Scout or the Basis 1400. Will they do the trick, or does it cost a lot more to get the level of performance I need?