Decisions, decisions! I came "this close" to getting the Mimas--what is it that you find it lacks (unless it is upgrade-itis)? I was intrigued at the tube preamp stage (and still am, now somewhat interested in the ModWright integrated which also has a tube preamp stage).
I also thought to do what you’re thinking, using a DAC with volume control and bypassing the actual preamp. That requires a good match with the amp iirc (impedance etc, things I am not expert in). The Spring 3 with preamp was my #1 choice for a time. I've been advised by people smarter than I that as good as a DAC with preamp or volume control can sound going straight into the amp, that a true linestage/preamp often adds more magic.
Synergy is so important. Do you prefer a more "lush" tubey sound with your Harbeths? My solid state integrated wish list includes either of the ones that Ayre makes... they sound or have more of the virtues of tubes, with all the benefits of solid state. Have you considered an Ayre amp? The VX-5/Twenty is on my short list.
I’m sure I haven’t helped much! This is the hardest part of hi-fi, sorting out the combinations and synergies. Good luck.