I mean, I suppose we could force it all to fit it if, say, Mirror Stamets, Mirror Landry, Mirror Georgiou (and who else am I forgetting) didn't really die in these episodes and Mirror Georgiou's sudden confusion at the loss of her future self's consciousness departing as well as injuries from killing Mirror Burnham caused her to relay a jumbled version (i.e. the "original" version) of these events to Michael in Season 1...
In fact since we now know Mirror Burnham was still bent on deposing Mirror Georgiou, it's completely possible that she secretly allowed Mirror Landry and Mirror Stamets to escape after healing their injuries, and likewise faked the deaths of a bunch of other co-conspirators she supposedly killed.
Doesn't the TOS/DS9 MU have to be a timeline where Lorca was defeated, though? Or at least didn't hold the throne long enough to implement his policies. I don't think high-ranking Vulcans were part of his vision. If anything, that's more like where the Empress was trying to go in TFpt2.