I used to barbecue a whole ham, back in the days when I had way too many deer on my place. What I learned was to do a lot of basting, and control the heat.
I'd start with the equivalent of "broil" heat from the coals. I'd baste and turn every three or four minutes until a good crust had started; usually some 20 minutes, mas o menos.
I used tongs, no forks to puncture and release juices. No salt in the basting mix, either.
My basting mix was whatever grocery store stuff was cheapest, and I'd then add whatever spices seemed "righteous". And some Lea&Perrins whigglewiggy and some butter and a little water. I'd keep it warm, there by the pit.
I'd spread the coals down to the equivalent of about a 300-degree oven after the crust had developed, and turn/baste every 20 minutes or so. About the time I'd need another beer, I'd turn/baste. Gotta keep the cook lubricated, right?
For a 10-pound ham (+/-), it would take somewhere between three and four hours to well-done but still juicy.
Backstrap? Cut on a slight angle, to 1/2" thickness. Make up a cornmeal batter and add some mustard. Roll the little steaks in the batter and drop into boiling grease until done. Serious case of the yummies!
Inner tenders? Cook slowly and gently over charcoal. Super splendiferous!
The rest of a deer makes for deer-burger, chili-meat or sausage.
Deer-burger has a synergy with tomatoes; makes some of the best spaghetti sauce you'll ever taste.
, Art