Tube Preamps.....

Pretty simple choice.

1. Primaluna Prologue prem tube pre amp.
2. Denafrips Ares DAC.

The two items will come in just under your budget. The Ares is a giant killer of a DAC.

With the Adcom amp, I think you’ll enjoy the tube preamps that lean more on the "tubey" side of neutral. I have an Adcom GFA-555 that has been paired with my GFP-750 for many years and I recently bought an Aric Audio all-tube preamp for another system and I really like how it sounds with the Adcom amp. It gives it a nice lush and engaging tone, particularly in the midrange, that the Adcom preamp lacks. Some may say its not neutral but it just rounds off the edges without losing much detail. I think you’ll be delighted when you put a tube preamp in front go your Adcom and for $3K, especially used, you can get something real good.

Yes with the 565’s being heavily modded by Musical Concepts that made a huge difference in the way they sounded. They never were as bright and leaned on the more neutral side then other Adcoms. After the upgrades completely different amp. I have a friend that has stock 565’s and they sound much better with tubes. that was why I was leaning towards a tube preamp. Thanks for the responses. 

I highly recommend Don Sach's 6SN7-based tube preamp.  It betters any preamp I have had in my system and I have a boatload of them.  Don sells the preamp directly so they are an extremely fine value.  There are lots of review of the preamp on this and other forums.  

Atma-Sphere UV-1 and an Ayre Codex DAC would be my suggestion.
B