Looks like the "Ball, Dark Red Shiny 1 3/8" would be perfect, and works with super and competition bases.
Actually, ya know what, I think I ditched the ultimate sticks because I don't like them, and got competition sticks.... but I don't remember what I did with the 4-way, it might be ultimate still.... Anyways.... If it works with super and competition, it should work with ultimate, no?