Being stuck with 2 facelift E53 6-speeds is not really stuck at all. You will be able to sell one of them easily. But maybe not before you need to buy the new one...particularly in the middle of this pandemic.

BTW is the hitch OEM? Is the wiring OEM? The standard OEM hitch wiring was 7-pin

You should move this to the classifieds section with a bunch of pictures.