Normally I like your designs, and I would this given suspension of belief... The design itself is beautiful, but... Not continuative, at least in my opinion (if the Terran Empire still existed in the 24th century). Officially there is no more Terran Empire/UEP in the Mirror Universe and things have gotten a little less mirror-ish in the Mirror Universe... That's probably why I strayed away from canon interest in that area, as well as in others. I like the idea of what the Terran Empire/UEP (United Empire of Planets) would be like in the 2360s in a TNG novel called "Dark Mirror" (a ten-or-eleven-year-old novel) that showed a dying UEP and how it's desperately preserving itself (I won't spoil much, but I think laws of physics were payed closer attention, such as how the UEP's plans were carefully planned around the idea that if they just jump to our universe, the addition of so much more energy and mass, and decrease in their own, although could (unsure of that) be adjusted for, would be devistating in local space due to distortions and anomolies that would result in the unbalance of mass and energy, something from which you don't see in most time or Alternate Universe stories.
I also liked the idea of having the universes have subtle changes, but not much. While I believe the UEP is more war-like than the UFP, I don't believe they would have drastically-different starships, which is why I don't think the design would be plausable unless the UFP had one similar to this. And although like this, the Sovereign-class history on how it was designed and built is non-canon, I still don't like how it semi-mirrors the story of the development of the Galaxy-class Starship's development as being slowly built in similar a way. I figured like most FC ships that the Sovvie was a more-recent design that was drawn at least in the 2350s and built and released in the decade or two after, near the end of the 2360s...
The point in this being that I'm not real fond of the top of the warp nacelle being too Sovereign-esque (as well as the top of the secondary-hull), yet hypothesize your reply of being developed based on technology that was slowly developed and applied to the Sovereign-class development project.
However, if I shrug off all that fan-based stuff off my head and allow a suspension of disbelief for a second, I think I can enjoy this design, it is very nice. Aside from the top of the nacelles and secondary hull being Sovereign-based, I see design lineages from the Excelsior-class, Ambassador-class, and the Constitution-class, with more of the configuation of the latter class of ship. I really like it.