Well... yes... the Legacy Audio Calibre is an incredible speaker. I’m not sure I would consider it to sound particularly "warm" and "rich," nor would I consider the ATC’s to be. Though, few speakers sound as great as the any of the Legacy speakers (Calibre and up in the line), or certainly the ATC’s. If I had my choice... it would be the ATC 100’s and above.
But... if you want a speaker that has the "warm, rich" sound you’re after - without a doubt - that would be the Harbeth 30.1’s / 30.2’s. With the Hegel H390 / H590, or Mac MA252 / MA352 - they will sound just like your HD600’s (HD650’s with less bass and more balanced sound)!
The caveat is... you must drive them with those amps, or very similar SS or Hybrid amps, or they will not possess the clarity, dynamics and details you may want. I'm not sure how they would perform with the Ref 5SE into the Pass Labs 350.8.
I prefer the the preamp in the H590 in combo with the H590 amp and, perhaps, the DAC in that unit to my Ref 5SE into my AR Ref 150SE amp and Schitt Yggdrasil DAC. The Hegel provides a bit greater clarity, dynamics and detail than the AR combo when driving the Harbeths. It is possible your 350.8 may be too warm, or may not control the bass as well as the Harbeths need to provide sufficient clarity and dynamics. It's kind of like the difference between the clarity of the HD650's compared to the clarity of the HD600's - the HD600's just provide greater clarity, dynamics and details than the HD650's. But, if you prefer the warmer, more subdued sound of the HD650's, you may find the Harbeths are just fine with your setup.
But... if you’re after a more neutral sound with the ultimate in clarity, dynamics and details - without being strident (a la anything with a BE tweeter) - the ATC’s and the Legacy’s would be it!