In your budget, I researched vintage, multiple converters, anti-jitter, over-clocking, up-sampling, and other OEM tricks.
I searched and searched for a better sounding CD player, and succeeded with 2 excellent sounding choices within your budget category,
CD only, Onkyo Integra CDC-3.4 mark II
CD and SACD: Yamaha DVD-C961
coincidentally they are both changers, an added feature IF they sound great which either do.
the search
then I found out about SACD players converting DSD to PCM, and some do not,
then I moved up a notch
Sony xa5400ES, it's like buying my over 4,000 CDs and some SACD's all over again, I am buying CD's again it sounds that good. My/your expensive cartridge/stylus will not need replacement as soon when you have a great CD player and use it without hesitation!
https://forum.audiogon.com/discussions/sony-sacd-player-scd-xa5400es-yay-or-nay
my advice, sell something, get some more money available, find a lightly used Sony xa5400ES. lightly used because the lasers eventually get weak, I had that problem with an Oppo and a Denon.