If you ever buy a bare root tree, you will notice the roots have been pruned. If the roots do intertwine, you can just prune them, and it won't hurt them at all! I'd soak them, and get them untangled the best I could, but I wouldn't fear cutting them. If you do prune the roots, then also prune the top so there are enough roots to support what is above!
Lots of good ideas in this thread! Wish I would have thought to divide my big pots with 3 cuttings. I'm stuck with the above method for separation, but I'm cool with it!
Suzi