Sometimes your choices are few and you have to move on but I'm disappointed we couldn't be much help to you on figuring this one out. I think you definitely ruled out carburetion.
I know the sputtering Tecumseh engine is gone.
Here is couple of links to videos of how a carb MIGHT can be modded to fix a sputtering hunting engine that is running lean.
This is the basics to what I did to my HM100 Tecumseh carb idle jet.
My Tecumseh carb jet was similar to the Kohler/Honda but all brass.
How to fix/mod a one barrel surging Nikki carb used on Briggs single cylinder engines link. See post number 9 for the video