I eat a lot of 100% ground venison with no fat added.
If your heart is set on burgers then I would recommend you make smaller not so thick buggers, basically sliders.
A good way to do this would be to use your bacon grease in a hot skillet on the stove, get it good and hot. Form the slider patties, season and then skillet cook them... kinda smash burger style but without the need to really smash the crap out of the patty.
Sear em good but dont over cook them. The less cooked the wild game is the better it taste. This doesn't mean to cook it rare or anything, just understand that it doesnt take as much cooking and it cooks faster/harder than ground beef.
Honestly a better and likely more successful 1st time dish with 100% Elk/Venison would be ground taco meat.
Simply season with salt, pepper, garlic, onion, a little ground cumin, chili powder, and then add paprika in place of more chili powder if you don't want the heat from more chili powder.
Add a DRAINED can of diced tomato and chili as it cooks and u will have good taco meat.
Make taco salads, nachos, hard tacos, or get real flour tortillas and make good soft tacos.
This will give you some good experience on what to expect when cooking 100% ground venison so that you don't go in blind if/when you attempt to make burgers.
No matter which way you choose to go let us know what u do and how it turns out :)