I grew up eating moose. Mom was never into any meat that had any shade of pink! So it was always cooked long and low in the oven. Steaks were pan fried, with salt, pepper, sliced onions, browned, then covered, and simmered for hours till fork tender.
My self, with moose or elk, medium is perfect for steaks. You wont find much better any where! As for roasts, I treat them like brisket, or pot roast. Long, slow cooks. The meat is dry, so water, stock, and or wine in the roaster. Aromatics like rosemary, thyme, sage are great! When near done, throw in some carrots, and baby potatoes, cover, cook till done. Reduce the liquid for a sauce, or thicken with corn starch for gravy. Mom was a great cook, but it was salt, pepper, onions for just about every meat. That with home made bread, and fresh baked sweets, little wonder why I love food so much!