The fact that the meat smelled fine after thawing makes me belive that the smell released during cooking may be in the muscle and not on the outside. I would guess that it's due to an injury to that area  and is most likely confined to that section of the animal.
    Personally I would have no problem eating it, and would do exactly what you suggested as far a marinating.
    Ruth brought up another point, how did it taste? Every wild game animal has it's own smell, and we are all prone to compare the smell of wild game to domestic meats. The "faint bad smell" may be just the normal smell of that animal based on age and food sources.

Dave & Ruth
D & R Processing