God, we tried for years to make a good venison burger, just never found a way to do it without adding fat to it. Normally I'd say dice up some slices of bacon into fine chunks and mix that with an egg and some spices and diced onion into the ground venison, but you're not wanting to add fat.
How about some burger like alternatives?
My mom did/does something she calls quickburgers, it's just ground beef or venison, brown the meat in a frying pan, drain all the fat you can, add in a can of french onion soup and a little bit of Worcestershire sauce and simmer for 10-15 minutes. Serve on buns like manwhiches. You can use dry soup mix if you want a drier sandwhich (it soaks through the buns pretty quick). She came up with that when I was a kid and at times the only meat in the house was deer and god we were so damn tired of deer. It's actually way better than it sounds. That with just some home made fries is still a favorite of mine.
Deer hash? It makes good sandwhiches.
Meatloaf sandwhiches? Could even grill the meatloaf to smoke it, the bread crumbs, onions, pepper, eggs etc will moisten it up well. Maybe cook in the oven, slice and then throw on the grill to give it a little char and smokey taste?
If you haven't already ground it up I'd think deer might make a good philly steak, onions, peppers, spices, etc would cover up some of the dryness.
The problem with deer is you just never know what you're getting it could have been living off apples for the last month, or wild onions, and grinding it up and just throwing it on the grill doesn't hide anything taste wise. If you can marinate it, simmer it in gravy, cook it as a roast with veggies, etc it's all good, but just grind it up and throw it on a bun... nah, just not good.
