Are those two rivet holes the only thing holding this pulley and hook in place?

Rather than put a stainless strap around the mast I would put it over the top so it's anchored at the front of the mast and make it wide enough at the back so it covers the whole width of the flat area. It looks like there's still enough aluminium left to support the load from the mainsail. Just rivet the pulley to the stainless strap.

Before you do that make sure you seal the top. You will have to push a plug down past the corroded part, with silicon, and put a few rivets in for it to rest on so it can't be pushed further in to the mast.