I think the Queen is just an AI spread across the conciousness of the entire Borg Collective, or at least multiple subsets, with a full manifestation in the Borg Queen body. There can be any number of Queen Bodies spread across multiple Borg vessels & facilities, she just downloads a copy of her complete AI conciousness to that body and feeds back all memories & data to the distributed conciousness that is the Queen AI spread amongst the Borg Network. The drone body that was assimilated to be queen has some influence, but the downloaded queen AI is the dominent mind and does most of the decision making, over-riding the original drones conciousness most of the time. This will account for the slightly different acting and decision making by the various women who portray the Borg Queen.
That makes a lot of sense- particular with how the Queen was introduced in First Contact: the AI had just finished uploading into her head, and was being attached to the rest of the body.. dJE
It would've made sense if the Queen AI only rarely installed itself in a drone body when necessary for certain purposes, like in FC, but that's not the way Voyager went with it.
AI or no, I think it's clear she downloads herself into new bodies when the old one is destroyed. I don't think that accounts for the discrepancies in portrayal between actresses however, since the Queen isn't shown to have died at any point between "Unimatrix Zero" and "Endgame." Susanna Thompson and Alice Krige simply interpreted the Queen in slightly different ways, I don't think you can--or should--give it an in-universe explanation. Characters are recast all the time.