Since you have HQ Player, I would suggest you look for a used T+A DAC 200. It has separate processing paths for DSD and PCM and does spectacularly well with high res feeds from HQ player. Yes, I own T+A gear, but this recommendation comes with a lot of outside support. There are forums on audiophile style dedicated to the unit and HQ player you might want to peruse.
The DAC checks the boxes you list regardless of format (but is shockingly good on native DSD upsampled from HQP) and is within your budget pre-owned. At least worth exploring.
Best,