DD,
Which ever adhesive you choose (Shoe Goo would be my recommendations from my running days) be sure you have some small pieces of wood or another flat, strong material to put inside the shoe so you can put some C-Clamps on the shoe and heel. This is to make sure the entire sole bonds with the shoe, without any bulges that will telegraph to you feet. Hope the repairs work, the seller was a stand up eBayer.

Bill