Ok, we figured out the cause of the leak in the carb.
We disassembled it and inspected everything. The float height was fine. We even tested it by gravity feeding gas into the carb and watching it shut off properly.
When we put the little T piece back in it was a little high and may have caused the gasket to leak. In addition, I screwed up the tightening procedure, so that may have caused a leak too.
Anyway, we put it all back together and the carb is no longer leaking (yes!) and the engine hasn't stalled yet (PROGRESS!).
I did my best to set the fuel mixture and idle speed using a laser tach and a vacuum gauge for the mixture on manifold vacuum. I *think* I got it right, but I've never done this before so I'm not sure.
It now appears to be misfiring under load. Here's a video of it:
https://youtu.be/257T5fHbnE4
Is it possible this is caused by incorrect fuel mixture? Or is this definitely a spark issue?