Biohazard

Seems to be working. Like I said; stone cold, she starts instantly and fast-idles for 30-40 seconds. Then the gagging (best description I have) which leads to stall.

It was running great - no issues but I let it sit since last December so, when I tried to reignite, and it was doing this crap, I first suspected varnish in the fuel way.
But after tearing down and cleaning the carb, I can rule that out.

Could this be vacuum?

Vacuum, perhaps. Plug up all the ports on the intake and carb, and give it a try. If it shuts down, hook up a gauge and test it again. Just remember that you will definitely get bad vacuum readings from the gauge once the engine begins to stumble, whether it's a vacuum issue or not. The gauge will only tell you something if you get a stumbling needle before it begins shutting down.

Either way, it's quick enough to do all of this to rule it out (or not).

I'd put an in-line fuel pressure gauge on the system if this fails. At least to verify whether fuel is being delivered as intended.

-Kurt