Bud, I have a 13 hp honda that is hard to start. Honda says it's an easy start, yea.
I also worked on a vertical shaft briggs 15.5 hp briggs for my termite man. He said it had a bad starter. Come to find out he had a dead battery. Replaced battery, engine was locked up. I removed spark plug and motor spun easily.
The problem was, if the exhaust valve clearance isn't spot on, the motor will have too much compression and the starter won't spin it over.
I adjusted the valves, problem solved.
Check valve clearance. You can find the setting on line.