Match book cover is about .035, used to set points that way.
With a cold engine the choke should close .035 to .060. Smaller engine needs less, bigger engine needs more. The book will give you an angle to uses which is fine if you have that tool and training. If not ... When the choke is closed there still needs to be small space to let just enough air past the plate to start other wise the engine will flood. On a cold engine with choke closed see if the air gap will allow match book cover to pass or a 1/16 drill bit.
Some how your not getting fuel enough to start after it sits for awhile.
As suggested look for pump shot on cold pre start engine. You should get a good 3 to 4 pumps if enough in bowl. You can try the shot of starting fluid (ether) as suggested as this would rule out ignition or starter. With a bad starter on a hot engine it's operation usually gets worse, not better.
It sound like your fuel bowl is percolating off after shut down. Then when you want to start, you need to crank enough to push the fuel to the bowl and refill it enough for the idle circuit to pick up the fuel and allow the engine to start.
Check gasket under the carb. It should be about 1/4 inch thick. The thickness helps insulate carb from manifold heat and reduce the fuel bowl to percolate off. The fuel pump has a check valve and if that fails all of the fuel between the FP and carb will leak down. When this happens it will cause the issue you are experiencing.
Also check around the carb make sure there is is no obvious leaking.