Matt, I'm not so sure that dividing it would be the best thing, unless it's clearly two or more plants in the one pot. Mine was in the same size pot from the day I found it until it blew over 33 years later, but as I mentioned above, it seemed like it was finally ready for a larger pot before the mishap.
I never took pictures of it in its larger pot, so will get some shots that will capture the new growth from the snapped ends. It is much happier in its larger container.
I've never had my CC bloom more than once. I know some friends with a red orchid cactus (a started cutting that I gave them) that provided a second round of blooms during this past summer, though. None of my orchid cacti have bloomed more than once either.