Cut it and wait a week before putting in potting mix to root. Same with pups. Do it now. They need more light as they are growing thin and weak. The base of the plant will continue to produce pups once you have cut the top off.

So cut it right at the skinny part in the middle?

Yes

Can you take a close-up photo at the point where it bends over? That does not look like a rot. That looks like the plant was previously cut at that point and an entirely new section grew above the wound.