For now, go with the supercedure cells. Next time, don't cage the old queen. They know she's Momma, she won't be rejected. If you cage her, she stops laying, her pheromone production and other queen substance productions goes way down, causing her to get rejected.
You'll very likely get much better results than splitting by raising queens in a Cell Starter/Finisher colony and planting queen cells into queenless nucs, or re-queening with mated queens introduced in Laidlaw cages.
Splits have to go through a whole queen rearing cycle, taking them out of production for a month while the new queen gets going and laying a solid brood pattern before things get going good again. This hurts the population considerably. On a dry year, they can miss a big part of the only nectar flow in the Spring, leaving the split colony without enough stores for winter, and having hurt the mother colony that the old queen stayed in, too. There's a great book by Dr. Lawrence J. Connor titled, Increase Essentials that really explains this thoroughly.
A mated queen introduced in a Laidlaw cage is accepted soon after she starts laying eggs. Release her when they have stopped attacking at her cage and are trying to feed her. Presto! They're back in action making honey, wax, bees, etc., usually in less than a week. You may even get 2 "splits" this way on a good year. The Laidlaw cage is described and photographed in Dr. Harry H. Laidlaw's book, Contemporary Queen Rearing, or you can use the search box here on Beesource where I've posted it before several times.