The universe presented in "In a Mirror Darkly" is different than the one presented in "Mirror, Mirror" and it's sequel DS9 episodes, namely, the existence of cloaking devices. Therefore, one must assume that each alternate Earth has a mirror universe duplicate, along with the infinite alternate timelines, each being a subset of these universes.
As mentioned above, the MU had cloaking technology in DS9's third season episode Through the Looking Glass, and that was forgotten when The Emperor's New Cloak was written.
But regardless, the cloaking device used in IAMD was a Suliban one. In the Prime universe, Suliban got cloaking devices from the mysterious Future Guy from the 28th century, so presumably that's where they come from in the MU as well. See, that's easy enough to rationalize without the need to declare everything another reality.