I've just bought a (second hand) Gustard X26 Pro.
It sounds fabulous at half your budget - but probably equals or betters DACs up to 3500, maybe 5000.
Wide image, incredible bass, dense and open mids, airy treble, great resolution. No ESS glare or "coldness" whatsoever, quite the opposite, in my system it sounds fluid and organic.
since it is half the allowed budget, you can even add an external clock since t has a 10MHz clock input.