I think the Denafrips Pontus would be a great sonic fit for what you’re looking for, and paired with their Iris DDC you get a significant and very cost-effective performance bump along with the ability to take advantage of the i2S connection. Here are some nice used units available now that’ll save you some $$$.
https://www.usaudiomart.com/details/650097309-denafrips-pontus-ii-black-r2r-dac/
https://www.usaudiomart.com/details/650045633-denafrips-iris-12th-digital-to-digital-converter/
Pair this with a Pulse Mini and add something like a Teddy Pardo LPS to it and you’d have an excellent setup for about $3500. That’s what I’d do, but alternatively you could substitute this Audio Mirror Tubadour for the Pontus (but still keeping the Iris for i2S) if you’re looking for maybe more tube goodness and still be under your budget.
https://www.usaudiomart.com/details/650074205-audio-mirror-tubadour-iii-se-nos-tube-dac/
Just some ideas, and best of luck.