My favorite part on pigs and deer are the shoulders. I either smoke them whole or pot roast them whole.
In fact when my buddy was trapping hogs Id keep the small ones that he couldnt sell. Id give away the hams and backstraps and keep all the shoulders.
I brown them in a big roaster, then cover with sliced onions and bell pepper and simmer until the meat is falling off the bones. I pull all the meat off, Toss in some baby portabelas and baby carrots, and simmer til carrots are done.
That is absolutley my favorite way to eat deer meat and enjoy it more than grilled backstrap.
Only thing that comes close IMO is grilled heart steaks.