For SA, we booked the lodges and flights to/from lodges (but not our SA flights) through Amex FHR. I would not recommend doing that (though we did get free massages as an amenity). They are very inexperienced, or were at the time, in bookings and ended up outsourcing to a third party operator who held random dates we couldn’t get released easily and we almost lost our preferred dates. The pricing was also not transparent as they included at our request some tours of Capetown, but it was far more expensive than booking on our own. For Tanzania, we booked flights to/from Kilimanjaro on our own, and then directly with Singita (starting with pick up at airport, first overnight hotel, the lodges, and our flight to the Ngorongoro Crater area (manyara, I think?). Then And Beyond picked us up and transferred us to Crater Lodge and back to Kilimanjaro. You can actually book the whole thing, even And Beyond, through Singita. It was very smooth - even when we misconnected in Amsterdam on the way to Kilimanjaro and lost a night of safari.

there are a ton of Singita trip reviews on this board if you search.