Rupert's pretty much dead on. I don't add fat or bacon to my game burger. Quality olive oil mixed in just before cooking works well.
Define "gamey" flavor.
If one is talking about rutty animals, I've had some experience with that, unfortunately. (Not all animals obey the calendar - and I might have pushed things a time or two...)
If you are talking about the natural variance of game flavors- just don't hunt the things you don't like... I like the different species flavors, and have no desire to eliminate them or camouflage them with marinades.
As for the OP's flavor list, in my opinion, his taste buds are all ef'ed up.....
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For example, I'll take quality moose, caribou, white-tail, and mule deer in no particular order over elk any day. YMMV. I like pronghorn done right better than elk, also. Bison is below elk, Musk ox up with the first mentioned.
There isn't anything native to NA better than wild sheep or a young mountain goat, IMO
