You say the leak down test was oK, but the compression was only 15# probably due to compression release???
15# is suspect as too low even with compression release operating and the leak down could have occured with the valve seated good and gave a good test.
2 or 3 carbs later still same.
The engine was ran without oil is most likely a hint.
I would do another compression test with the exhaust rocker off the push rod. Do several compression test keeping a heads up for intermittent valve leakage, and watch the strength of the compression pulse as the engine turns over, like a seat loose and it don't take very much upset on those type OH valve stems and guides for a valve to slightly stick or gall in a guide, because the valve springs are not real strong. Push the valves down with your fingers and feel and watch for consistency in the two valves comparing one too the other. Also check for valve guide wear. We know that most likely it's either erratic compression or ignition. I assume you have installed a NEW correct type gapped spark plug. I've seen CHAMPION spark plugs act just like that.
But again that is the way the old L head Briggs
sounded when the magneto finally completely failed that I mentioned about but had more of a spit out the muffler.
You can take a Briggs type inline spark tester or Oregon 42-087 like this one and use in in a shade or dark place and carefully watch the spark while the engine is running. Do not relay on a bulb type spark tester. A engine will run normally with the Oregon or Briggs spark tester inline.
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https://www.ebay.com/sch/i.html?_from=R ... +&_sacat=0I don't like to just throw parts at something (unless process of elimination in this case and just a little bit bad)) but I suspect you can get a magneto for that engine for around $10 from flea bay. (and do try a new spark plug)
If it don't go then you eliminated most all except for valve/ erratic compression issue.