Well, I killed two Hyper Goombas, one of which was holding a Last Stand, and saved, then got a Last Stand after killing the third. I re-loaded and killed it again, but didn't get the badge. So unless in the most trollish of moves that third Goomba dropped the badge, it unfortunately appears that badge drops being pre-determined is out.
Which, incidentally, makes me more skeptical of item/badge drop likelihood being related to the number of the enemies in the battle. I'll still believe that all enemies' drops have a chance of showing up after battle, but badge drops almost definitely aren't determined upon killing them (I might try the experiment until I get a couple more Last Stands, but the chances of that one being dropped by the third Goomba are quite implausibly low).
Coin drops definitely are, though (well, there is a ludicrously low chance of those values being a coincidence, but it certainly seemed legit to me, seeing as the value changed as soon as each enemy was killed, and the total at the end matched the number of coins dropped exactly four times). That's so strange...
Curse you and your emulator-unfriendly item-drop routines, IS.