Briggs engine on Toro recycler mower is possessed

[bwright1818]

I have the above mower. Not sure what model Briggs it is, but it has the automatic choke connected to the muffler, with a control rod. Symptoms vary. Sometimes it starts and runs. Sometimes it doesn't start. When it does run, it will sometimes go until I have to empty the bag, then it won't restart. Other times it runs for varying lengths of time, then begins to misfire, getting worse and worse until it quits....BUT, if it's in this mode, if I stop pushing the mower, it smooths out for awhile. It seemed to me like the coil was failing, so I found a used one on eBay for ten bucks. This SEEMED to work better for awhile, but then it started causing problems again. I had noted that there had been a number change on the coil, so I bought a brand new one for $32 from Partstree. This included a new stop wire, which I installed. It started and stopped as a test, about ten times, flawlessly. Then, when I went to actually mow with it, it wouldn't start at first, then started, ran well for a few minutes, then started misfiring randomly for awhile and quit, with the same condition as originally occurred, where it would run better for a while if I stopped pushing it. I should just throw this thing in the dump; but now, it's personal. Any ideas welcome.