You say the “splits would have to raise a queen”
Depends on how many hives you want. Obviously you are going to split for at least three colonies.
What would I do? I would remove the queen on a frame of brood and one of stores and place in a nuc beside the parent colony. After four days, I would select good open queen cells from the parent colony and make sure there were two queen cells left on the frame(s) chosen.
These would be put into nucs with as many nurse bees as possible, in order to nurture the queen cells properly. At this point, I would transfer the original queen to the parent colony (ensuring no queen cells and move the new splits away from the parent).
The flying bees would return to the old hive the following day, leaving the nucs in need of some extra feed, possibly on day six, along with a check on all parts to make sure there are no more queen cells drawn.
Then leave them alone for three weeks, or so, before inspecting.
When queens are laying and her new brood has emerged for at least a couple of weeks, get rid of any queen that does not meet expectations, by uniting as necessary or replacing those queens with fresh stock.
The new colonies may need a lot of feed , by then, to expand for the winter. Transfer to full hives as they become stronger or take them through the winter as nucs - your choice.
Might be some precautions necessary to get this plan right, but you should at least end up with two viable colonies with decent queens.