DAC recommendation

Unfortunately, as you go up the model line, the better the sound reproduction.
I have owned almost all the Schiit line. From Modi to Gungnir.
The Bifrost Multibit is probably the best buy, but at $450 used, a little over your budget.
The Modi Multibit is certainly in your budget, and I think you will be happy with it.
The thing about DAC's is that they are moving at a fast pace regarding sound quality reproduction, so I try to find a manufacturer who will offer upgrades.
Both Ayre and Schiit do so, and are the ones I buy.
B

@OP,

a DAC that would make Tidal and FLACs sound equally musical and engaging. And wondering if that exists for $300

At $300, it might be possible, but I rather doubt it.
B