If you are getting regular blue spark, then I think it must be in the fuel.
While turning it over, I used to short each plug with a screwdriver to make sure each plug was getting fire and getting it evenly... Or just pull the wire and stick a screwdriver in the end and let it short out to ground. Sometimes easier to see in low light.
I've seen a lot of weird "low-probability" things like stripped drive gear on a distributor, stripped rotor, etc, that let the rotor jerk around some - distributing some fire - but not that would let the engine run.
BUT, if it sounds smooth for those 4 seconds, I'm guessing all your electrical and mechanical is all good and you just need to figure out the fuel issue...
Could you post a pic of your regulator??