Cutting your pot sounds like the best idea. One thing to note is if your plant is truly root bound, it will not continue to get bigger even if you replant it. A way to fix this is you need to cut some of the root system. This will trigger the plant to try and fix and reestablish the roots that were destroyed. Then the new roots will grow into the new soil and continue growing.
Don't cut any of the roots in the top soil near the stalk, you don't want to ruin any of the feeder roots. Once you peel that pot off, just stab some scissors into the very bottom in a few places, and maybe from the side in a few places. Don't get crazy with it. I would say about 10 stabs total, only where you see thin roots. You will see your plant start growing again in the next few days. I've done this quite a few times