Carbs sound gummed up suggest full carb rebuild
I wonder how you can diagnose that from just those 6 seconds. Your suggestion is a bit drastic, isn't it?
I'd follow Cal's suggestion. Verify all floatchambers have sufficient fuel. Actually, from what I hear, it sounds like you're almost there. In your case I would not hesitate spraying some Startpilot to the airintakes.
What wouldn't harm after months of inactivity, is: drain the floatbowls, keep the petcock closed, turn the 'central' idle adjuster knob (on the right side) so, that it will
lower the gasslides, close the chokes, and then crank, either kick or electric, the engine and hope the underpressure will suck the slow jets clean.
Spark on
all 4? Sure?