Thanks everyone for all the great suggestions. And yes, this is a problem I don't mind having! The majority of our meat is whatever my husband has shot, so I'm used to cooking with venison. I have found moose to be very similar. I normally use ground venison for chili, barbecues, taco meat, and other dishes that don't require the meat to hold together well. The grated vegetable idea is especially intriguing as I'm always looking for a way to get some more veggies in our diets.

Use a cooks illustrated trick for all beef meat loaf.

Gelatin. A 1 tsp of unflavored gelatin to 1/2 cup of broth. Let that 'bloom' about 15 mins or so and add that to the cracker or bread crumb mix and then make the meatballs.
The gelatin replaces the fat in lean meat.

KTR having moose in your freezer makes you automatically awesome :-) re:dryness - grated vegetables will help with that - try grating onion and maybe caramelizing it a bit then adding, also grated zucchini and/or carrots - the zucchini will have the last impact on the flavor of the meat, so choose according to what flavor you are going for. You could add apples and herbs too - you get the idea!!!

What a nice problem! Or, maybe it doesn't feel like that now...
Anyway, if I had your stashes, I would use it as an opportunity to learn traditional recipes from places and times where these meats are regularly eaten.
For venison, Perigord or other areas of France, for example:
http://www.frenchconnections.co.uk/blog/french-recipes-to-love/1778-venison-daube-a-winter-warming-recipe
Or Britain, for example this one from Scotland:
http://www.bbcgoodfood.com/recipes/1935/succulent-braised-venison
For moose meat, Canada (especially hunting and fishing lodges where they cook what they bring in) or Scandinavia (Noma and other innovative restaurants).
Even if they don't use ground meat, you can still adapt their seasonings and fats to the ground meat you have.
Looking forward to hearing about your results.

Moose meat is very lean, so if you don't want to add a protein with higher fat content, maybe soak some cubed bread in milk and add it to the mixture and eggs would not hurt.