I have a MTD tractor with the same B&S engine with the same problem. I replaced everything I thought I should replace to get it to fire. nothing worked.
It now has 2 flat tires from sitting for a year. You've taken the diagnostics to the next level.
If you ever get it running, please post your solution. Mine was buying a $150 push mower


George Freelance Observer 07 BA with 605's, engine dresser bars, and cheap saddle bags.