It would make sense if the ENT mirror design is different-looking. If I remember right, the ENT-D from TNG: Dark Mirror was actually supposed to resemble a Sovereign-class. (Albeit a LOT bigger!)
Not a Sovereign-class, because Dark Mirror
pre-dates Star Trek: First Contact
by two years. But I was always fascinted by the Diane Duane's vivid description of the Mirror-1701-D (p. 61/62):
It was the Enterprise. But not his Enterprise. It had a dark grey, even enlarged, a gunmetal color, cool and unfriendly. The design was overtly the same - the great sloped disc of the primary hull, the nacelles, the secondary hull all where they were supposed to be. But the secondary hull seemed larger; the nacelles were raked farther forward, and lower. The primary hull's curve was deeper and now had a frowning look about it. If ships had expressions, this one had it's eyes narrowed. It was a cruel look, and intimidating.
Sent chills up my spine when I first read it.
I stand corrected, though it might at least have some elements of a Sov.
By the way, that description of the mirror ISS-D is beyond epic.