Cam lobes and lifters look a little worn but not bad.
If the Intake valve is not seating correctly it will cause the Carb to leak no matter how many times you rebuild it.
You need to lap your valves real good and check your clearances again.Model 320000 Briggs valve clearances should be (Intake .007-.009) (Exhaust .017-.019)
I'm betting that after you lap your valves the intake valve will be rite in spec but you will have to grind a little off of the exhaust valve stem.
I had the same problem on my SS14.Carb would puke fuel all over the place until I lapped the valves.I had to grind my exhaust valve stem down almost .010.It's because over time the seat gets a little worn from the heat and the valve smashing down on it.The seat might have overheated a few times if it was run lean.
Do you have Both governor springs installed? They have a Hi Speed and Low speed governor spring.
Here's a couple good videos on the Governor and how they work and how to adjust it.
Here's how you set your Governor.
It wont lap down any more