Best sounding CD Players with Variable Outputs to use Direct into Power Amp?

I've run several cdp direct over the last couple of decades, almost always with excellent results (the only one that benefited from a volume control upstream was the Consonance SACD 2.0).  Your price point could be a bit tricky though.  You might find a Theta Miles or a Resolution Audio CD50 for that price but such an older player may likely need a new laser or transport soon.  I would be hesitant to purchase without replacement parts available so that's something to consider.  For a little more money, you may be able to pick up a modded Oppo BDP-83SE.  These are quite a bit newer and parts were still available last I heard.  I have a couple of these modded players, one from Modwright with the outboard tube power supply, and another from the Upgrade Company and either will stomp the Miles in terms of resolution/detail though the Theta has better dynamics and bass weight/slam.  I think I paid about $650-700 for the Oppos (each).  Do keep in mind that the BDP-83 (non SE) doesn't have the Sabre DAC like the SE version.

A little late here, but I use a Resolution Audio Opus 21 directly in to my amps. Before that I used a Resolution Audio CD50 sometimes direct. Both players control volume in the analog domain. The Opus 21 sounds wonderful this way.
The older RA cdps can be found in your price range.

There is usually a RA Opus 21 for sale over on Audio Asylum- Asylum Trader (classified section).  Happy Listening!

FYI..Have a GNS Opus 21 , and last spring Steve Huntley at Resolution audio installed a new drive mechanism for the CD, and it's still in the box!Never played since he sent it back, as I have a Modwright 105 that sounds great and plays video as well))..As long as they are around, I wouldn't fear buying one of their older players . The direct in gives you more money to spend elsewhere.