cactus loving stranger
It looks like it may be Escobaria vivipara - the brown central spines are normal. Even though you are breaking every rule to growing a healthy cactus, your's seems to be doing well. Still nice and round and growing offsets.
Cactus grow slowly - patience required. I don't bother to repot unless: 1. the pot is tipping over or 2. the cactus is going to suffer if it doesn't have more surface space.
I would repot and now is an excellent time. Find a pot that is about 1/2 inch larger all the way around and is wider than it is tall. The best pot material is un-glazed terra cotta. After you repot, watch the water. Use a cactus growing soil: fast draining but able to re-absorb moisture when dry.