What high-end cdp for low-end quality CD's ?

The Audio Synthesis DAX Discrete handles less than stellar CD's with aplomb. You could purchase their Basic DAC with your budget. If you want a digital only system perhaps you could apply your preamp budget and go with the Variable model direct to your amp.

Well, I own a Wadia 861. I've had it for 1 month now so my experience is not extensive. A lot of my CDs are also from the BMG & Columia House CD clubs. Most of the CDs are post 1990. I also have music on better quality disks. I usually go for the music rather than the CD label. It is a bonanza for me if I can get my music on a good CD label.
I do have some older CDs like Heart "Dreamboat Annie", Andreas Vollenweider "Down to the Moon" to name only 2 that are 1986 & 1982 resp. The Heart CD sounds very good thru the Wadia & the Vollenweider CD is also good sounding but it doesn't hold a candle to.......................the vinyl copy that I have of the same album!!
When I hear the Down to the Moon album I'm immediately reminded of the sound of the vinyl equivalent & I am disappointed with the CD. However, my disappointment is CD vs. vinyl (the age old peeve!) & not CD player-to-CD player.
FWIW, I think that your CD collection will sound just fine thru the Wadia.
I agree with Lugnut that any hi-end CD player will not make your badly recorded CDs tolerable.
A tubed output stage will have a diff sound from a ss machine. However, tubed gear can also be designed to be neutral in which case don't look for forgiveness there either!

You might be surprised how good your bad CD's will sound on a good player. When I moved from older Theta source gear (poorly recorded CD's sounded quite harsh) to my current Resolution Audio Opus 21 cd player I was surprised how much better some of my 'bad' CD's sounded. If you are able, try out some of those players on your list.

It is a myth that a good CD player will make bad CDs sound badder. I have CDs of bootleg recordings from the 1920s. They sound (relatively) fine. I also have alot of CDs from the '60s on forward. If you have a system that highlights the high-end of the spectrum, the deficiencies of the recording might be more noticable. I guess the question is whether you want something that will mask the sound versus the truth. My current cost-no-object system plays these deficient CDs much better than my previous system. If you get the Wadia and only play CDs, you can skip the preamp.

Get the absolute best sounding CD player for your system. If your system is reasonably well balanced, then badly recorded CDs will sound like badly recorded albums, but only in rare cases will they be unlistenable. If this sounds like too many "ifs", then an outboard parametric equalizer is very effective at reducing high frequency harshness and/or tubby bass.