I am having this same problem on a Briggs and Stratton Platinum. I haven't turned it over with a drill, but it has 10 PSI of compression. I'm going to take the cylinder head off and see what I find...
I'm sorry to hear you have this problem. If you read post 23 and post 18, you will see that my problem was entirely a compression problem. It was stated in one of the first posts and then again in a later post that the compression was much too low. After I got the new valve installed, I posted the results of the compression. You can see that they are much higher than originally and much higher that the 10 lbs you have stated on yours. I have since invested in a
leak down tester and used it 3 or four times. It wasn't very expensive but has helped guide me to troubles and pinpoint the troubles section of compression problems, saving a lot of time. I think you can check one out for free a few days from O'rielies auto store.
good luck with your trouble, and keep us posted on what you find.
Our mower has worked great now for the second summer. still starts on the first pull no matter how long it has set without being used. it even started on the first pull this spring after filling the tank and checking the oil.
Rex