It looks like the Merc got a reprieve.
The new carburetor arrived today and I slapped it in. I'm a pro at swapping it now. The idle was definitely smoother, but for the real test I closed the low speed air mixture screw 1/4 turn. Lo and behold, the motor started to sputter and die, just like the shop manual said it should. I put in a new set of plugs and then Aaron and I went out for a trial run. It ran great at everything from idle to wide open.
So the Mercury lives to die another day and that little project gets checked off our Bahamas TODO list.