Do you have a Briggs service manual? Just wondering as that is where I got the .30 figure from, it's used pretty much for any of the flatheads. If you don't have it, let me know and I can upload the .pdf I have and share it with you.
You are right though, Briggs usually can still run even with several things kinda out of whack. A spark tester is still a nice thing to have around and they are cheap enough, it isn't a huge investment. A leak down tester would do a quick tell on the state of the valves, head gasket, and rings sealing but without that the Briggs manual tells you to just kinda hand spin the flywheel and check how much it "bounces" against the compression (i.e. it should easily spin by hand).
Another thing, as another poster noted, a partially shorn key can drive you nuts with everything else being good and the engine still not running.
OH, one more thing I thought of, make sure the spark plug wire isn't grounding out anywhere on the tin or block. A lot of times, the wire can rub where it comes out of the tin and short there. Some electrical tape or a piece of that corrugated wire loom stuff prevents that. There also is the shut off switch wire that comes off the coil-it should go to a switch but if not, make sure the bare end isn't touching metal anywhere.
Also, here is the link to a troubleshooting chart I uploaded-it's kinda simple but handy as a checklist to go over:
Troubleshooting Non-Starting or Poor Running Briggs & Stratton Engines FORM MS-6605-2/01
I applaud your stick-to-it-iveness to get that old iron back alive! :thumbsup: