Whilst a bigger tenon is a very good thing, and I would certainly go that way, if you dowel it to the existing neck, there will be a weak point right where it has failed before.
I would be inclined to cut away the base of the heel parallel to the fingerboard for about half the depth of the heel then glue on a new piece of mahogany to form the heel and tenon.
This will probably look better than patching the dowel hole and will certainly be stronger