All of the best sounding systems I have ever used or owned , or heard had one thing in common. A great preamp. Usually the most expensive component in the chain. I had a Zesto Leto for a short time and it completely elevated the performance of everything around it.
Your original target price of $4k seems like a lot now but you’ll soon forget about the price if you buy something like a Backert or CJ. Or whatever suits your taste.
I have a RME DAC that I tried running direct. Boring. Put a great preamp after any good DAC and Bam…. Much more realistic I retired that DAC for a fixed output tube DAC and it is sublime