Having browsed through the manual online, I wonder if the CVP-201 has any graded hammer action..?
Maybe you should read the manual through
I guess the current CVP-series go over your $2000 budget, but here is my view: Out of the new, modern CVPs I think the CVP-405 has the best price/performance (String Resonance + 4 channel sampling), with exception of the CVP-509 (though costly), and with the CVP-505 being a disappointment. The CVP-407 is also good, with its additional iAFC (sound-to-room-dimension adjustment) over the weaker, but price favorite CVP-405.
Otherwise I would say the CLP-series is worth taking a look at, but you will lose all the hundreds of synth-sounds that are in the CVP-series. Depending on you local dealer's prices I think you could go for either the CLP-340 or the CLP-370. You can compare features in this link
Out of the Casio models I think the PX-830
fits well into your budget and the PX-830 makes a fair game compared to equally priced Yamahas. If you want more tones/voices (like the CVPs) you could go for the more expensive AP-620
, which hopefully should fit your budget.
If you still want many sounds/voices/instruments, the Casio piano-synth with 670 tones/voices, but weak speakers; the cheap CDP-200R
could be an alternative (probably ignoring the CDP-100 as it has few voices/tones).
There are also some Korg digital pianos worth looking at, the simple but heavy keyboarded; the Korg LP350
and possibly something from Roland (some feel Roland has a bright sound, including me, too bright sometimes, others like Roland's brightness).
There seems to be some kind of opinion in the forum threads that the Kawai keyboards have the best feeling in their price range competing to similar CLPs/CVPs. So you might look out for a not-too-old Kawai as well.