In a different Agon thread about DACs (there are multitudes) a member cited a video from Pearl Acoustics dealing with the question of whether DACS sound the same. I thought it was a thoughtful exercise and he minimized the hype. https://www.youtube.com/watch?v=TAOLGsS27R0&t=1229s
A second interesting source of information is from the Arizona Audio/Video Club. They did a blind test of several mid priced DACs and the results were interesting. https://azavclub.com/what-is-new-1 The Black Ice Glass Tube DAC, the Chord Qutest, and the Schiit Yggrasil did well but it was obvious from the results that there was not a clear consensus. I bought a Black Ice based on the results and I have been happy with it.
I have 3 DACs, 2 HDCD CD players, one SACD player, and a transport, with some dating back to the late 90's. I can say from my personal experience that there is a narrow range of difference between these units. Part of this could be that I'm 67 and my hearing rolls off over 12 kHz but I doubt you will hear any sort of dramatic difference with a new DAC. That being said, I'm planning to purchase an Audio Mirror Tubadour IV SE because I want to try a NOS ladder DAC. I can't audition this unit before I buy it but it has been favorably reviewed and there are several positive comments from owners on this forum so I'll take my chances. It is a little out of your budget at $3500 but still in the ballpark.
The other thing I'll mention is that there are a lot of used DACs on the market. You and I aren't the only audiophiles chasing the digital holy grail. This is a great way to experiment with different design philosophies without very much price risk.