When to repot rhizomatous begonias?

I have two begonias that have somehow been thriving for a couple of years. They are now trying to escape their pots. (Photos taken outside, but I usually keep them inside, in self-watering pots with grow lights.) The roots aren't coming out of the bottom, but the rhizomes in both are hanging over the side of the pot by a few inches.

The first one was just labeled "Geometry." It has never flowered but it has a very thick rhizome that looks like a furry lobster and kind of gives me the creeps.

The second is a hardware store Rex that stayed alive despite me living in a desert. It has constant flowers and leaves bigger than my hands. It's a little droopy right now because I had it hanging up high in the winter due to space, and the grow lights hit it from the side.

I feel like they're doing well and I don't want to stress them by repotting unless I have to. How far can the rhizome hang out of the pot before it's a problem? The Rex does goes through water pretty fast, even with the water reservoir.