+1 for the Ayre CD player...
I have the Ayre_CX-7eMP. When launched, it was a "Class A" CD player (Stereophile magazine). I love it and have no need for a separates (DAC + Transport).
Today they sell for very little (relative to your budget), if you can find one - usually ~$2k. . A non-MP version is currently on AG for $700 (asking price - 3rd PRICE DROP Ayre Acoustics CX-7e For Sale | Audiogon).
Prior to a purchase, a quick call to Ayre will confirm the cost of an upgrade to the "MP" version, including a full bench-test. At that point you know what it would take to have an up-to-date, reliable, and serviceable unit (at a pretty low cost).
Mine is not for sale, and I am not connected with the above mentioned offer.
Good luck with your decision...