Throttle wide open 3 full pulls is correct for compression test. now I am wondering if it is out of time too, you would probably have to pull the engine to check, its possable the the the crank went of of phase. The cranks are pressed together so you can install bearings and the press fit can slip, not sure how to check with engine together, maybe someone else has an idea.
The reeds will be between the carbs and the cylinder, I would think that the pedals would have to be really screwed up to keep it from starting though.
One more long shot is look on the front of the block to see if you can access the crankcase drains down low on the block and open them to make sure the crankcase is not full of gas, then drain the carbs, then pour a table spoon of known good gas and give it a try. that would insure that a slug of really bad gas or water isn't sitting in there.