This is how I do my venison, elk, moose, caribou etc roasts. They always come out very moist and are never dry.
I season the outside of the roast with my dry rub or Montreal steak spice. I cook it on my Weber gasser. I have one of the older Genesis models. I remove one of the grills and then centre the other one on the bbq. Under this grill, right on the flavourizer bars, I place a baking pan that I keep filled with boiling water. On the left side of the grate I place a foil pack of smoker chips over the burner tubes. I generally go through 2 pouches. I leave very large air holes on the topside of my pouches as I want thick smoke.
I get the bbg running at 350F and then place the roast over the water pan and hopefullly the chips have started smoking. I use a wireless thermo to monitor my meat temps and set a target of 135F. It usually works out to close to 15 mins per pound at that temp. I pulll the roast off of the bbq and tent it with tinfoil on a wooden carving board (so it doesn't lose heat as fast) and leave it for around 1/2 hour before carving.
The roast always comes out very moist but on the rare side (I think it shouldn't be any other way for game - excepting wild boar and bear and always has a very nice smoke ring. If you want to save juices for gravy or au jus then place the roast in a very shallow pan (if the pan is too deep the roast starts to steam in the pan).
Then carve that wonderful piece of meat and enjoy.
Ken