Well, I'm going to plug my favorite audio manufacturer once more and recommend this player:
https://athena.safe-order.net/decware/SACD/sacd.htm
It seems a bit over what you want to spend, and I really hesitated to buy it for some time, but I have amps (times two, and have had another of the amps as well) and speakers from this builder and LOVE THEM WITH ALL MY AUDIO HEART, so I began to yearn for a source from him as well.
This is a Sony universal changer with a tubed output stage modified on that comes right off the DAC. It plays dvds, SACDs and cds and cdrs with MP3 burned onto them. It took about five weeks for the tube stage to really burn in and bloom. . . but man now that it HAS it is the best source I've ever had in my home. Regular cd playback sounds really wonderful, and a good SACD is the step beyond it should be. The stock player that it is built around is quite good as well, and all its outputs are still active, but the tubed output trounces it. Coming right off the DAC gives really a dynamic and detailed sound. I'm really happy with it after a month of wondering if I should have gotten it; after three weeks it started sounding really good, after five it shined brightly and now I'm in my sixth week and wanting to play hooky to stay home and listen. I think because he uses really oversized powersupplies all his products seem to take a really long time to break in. . . but the wait is worth it.
Recommended, and there is a forum on this site that will have testimonials from the owners that gives good information as well. . . .