Ben wrote:

My question: Is there any hope for the rest of the cactus? Its all looks
healthy enough. Can I put some rooting hormone on the bottom pad? Will it
take?

I'd say it is worth a try. Opuntias are generally fairly tough.
Cut off the rotten "pad" and also the next one to make sure that
all of the "rot" is removed, and put the rest in fresh sand. Some
rooting agent can help, but it is not really necessary. Discard the
old substrate and replant the other cactuses.

Jan-Martin