.003 intake
.005 Ex
Intake is the main one to get set at .003-.005. go for .003 because the ACR (Automatic compression release) is on the intake cam lobe of the valve
BUT
You say the engine cranks fast which indicates that the valve lash may not be the main problem YET. (but can be easily checked)
You can see you tube videos of how to do such for your Model Briggs))
You say in post #7 when it's cranking fast you see gas blowing back up into the carb throat. seeing gas blowing back is normal on that Model engine when the engine does not start and it's getting too much gas into the carb float due to flooding.
The reason you see a spit back of gas is the ACR momentarily blows excess gas back into the carb throat and then sucks it back just before TDC for a run. (sounds strange but true)
Pull the spark plug and see if it's wet. dry it off and re-install then
turn off the gas supply to the carb set the throttle to high rpms, no choke and crank engine and it will probably start and run for little while. If you then see it doing same thing again the carb bowl is getting too full. Note that I did not say it's the needle/seat. If it's a Nikki carb the little rubber gasket in the very top of the carb above the plastic piece is bad (it seals above/before the needle/seat or the needle/seat is bad.