I am pretty familiar with the gear in your system and your criticism of the Chord is just how Chord DACs sound. It's not bad, just fits in certain systems and not others.
There are a million choices on the market and in your price range with that gear I would look at Playback Designs MPD8 which is a lovely DAC for the money and rivals units that are quite a bit more expensive, especially for DSD.
Linn, a Dual Mono Organik Selekt DSM in the Edition Hub format (this is a very customizable DAC with 120 combinations that can be made) but it is a stellar DAC/streamer that I find is an unusually good value and sonically will be an excellent match for your system.
For a more obscure option, Orpheus makes a stunningly good SACD Player/DAC that would sound great in that system. Model is the A Zero PS. I believe this uses four FPGA chips per channel and is very good sounding.
Weiss and dCS will not be materially warmer than your Chord. MSB would be an excellent choice and one I would definitely consider. Lampizator DACs are wonderful sounding but tube rolling can be costly. The new Rockna Wavedream Reference Signature would likely work but it is not likely you will get one used as it just launched an it is a hair above your budget.

