Good News:
Alright, the ignition came today, and the good news is it works! Even with the old spark plug. SO, I guess it was the ignition. Even off of only 3 volts, I got plenty of spark, so I'm pretty sure that part is done. Additionally, it is much smaller/neater of a package.
Box it came in:
AND installed, it only took a few minutes! The +/- battery connections go in two of the screw-terminals, and the contact goes in the other. I'd already had the contact wires done, so that was not a problem.
it ALSO came with a separate ground wire (likely for the spark plug, which I just hooked up to the edge of the motor for now. The one downside is the spark-plug connection is an alligator clip, rather than something nicer. Otherwise, it worked a charm! It says it can go from 3-6v, and the battery pack it came with uses 2 batteries, so I'm at ~3.2v.
Bad News:
No Fuel. The carb doesn't seem to be carburating. My check valve is doing something odd as well, I manually 'sucked' fuel up, and it seems that the check-valve keeps a vacuum behind it, but doesn't stop the fuel in front of it from going 'down'. I'd tested it in advance, so I don't know what is wrong with it.
That said, the carb isn't sucking fuel at all. Do I just have to figure out how to get the check-valve to do its job and 'prime' the carb in some way? Anyone have ideas? Or did I just screw up making the damn'ed carb?