Stone,
On edit, I've added a few more thoughts...Based on my limited experience with venison, I'd opt for backstrap (tenderloin) on the wsm at high temps., grind up the balance for chili and sausage. I've cooked backstrap a number of times and used other cuts in various recipes. Proper handling of the tenderloin will optimize the quality of your meat. I don't hunt, so I can't help you with those points; but I do have friends that have told me countless times you can really tell the difference between a properly butchered deer and one that wasn't. The bottom line is the tenderness will suffer if care is not taken.
Venison is very lean so with the backstrap, make sure you do not over cook it(keep it to med at most); otherwise it will be tough. I prefer to grill it, but that can be easily done with the wsm. Drop a piece of your favorite wood; pecan or apple maybe, don't use water, sand or any other heat sink and grill it to med-rare. Natural accompaniments with venison are: apples, cherries, red currants, juniper berries, mushrooms, black pepper, thyme, red wine vinegar and red wine. Using a few of those ingredients you could come up with a rub and a finishing sauce. Here's one sauce courtesy of Charlie Palmer:
2 C Beaujolais wine
2 finely minced shallots
1 herb sachet including thyme, bay leaf, peppercorns
1.5 C good venison glace or veal glace
Begin by reducing the wine, shallots, and sachet to 1/2 cup of liquid. Add the glace and reduce by 1/2 (about 20 minutes at medium simmer). Skim the sauce and strain into a bowl. (There are many recipes online for a
glace. Substitute the veal in this one for venison. Or adapt this recipe using beef broth.)
Paul