Merry is the lamb--gaminess/cooking temp

While I would oft-times sooner watch the James Frey-like fall that is the latest Diane Keaton film than let lamb pass these fair lips, I found myself throwing a bone-in leg of lamb on the WSM yesterday, after a basic marinade of lemon, garlic, oregano, mint, and, er, gin (I'm moving, and was rather uninclined to down the swill some unfortunate friend of mine--unfortunate that I have friends like this--had bestowed upon me at a dinner party I lately threw).
I took it off at a temperature that had rendered much of the lamb spot-on medium rare, if not some of the sea-jelly-like fat pockets around the bone.
The point is this--the medium-rare to rare portions of the lamb were wonderful, lamby but not too. The other, more-cooked portions were, well, what i imagine muskrat to taste like--just too damn gamey (though I hate this word, because it says virtually nothing other than that a flesh tastes significantly different than cattle, or chicken).
In eating beef, I oft-times think the rarer beef gives a much closer approximation to the taste of "beef" than those woefully brown/grey/black sections, but maybe that's not the case. After all, it can be argued that a good beef stew often gives a greater "taste" of beef than steak tartare, though I'd think to argue that this is the cut, rather than the amount of cooking.
What gives?
I could probably read Harold McGee about such a query, but what's the fun in that?