I'm not clear on why you would want to fix an engine that is rare without being good. Unless you hope to make a collector's item of this mower, it seems to me to make more sense to pick up a decent full-crank Victa 2 stroke or a B&S 4 stroke (around here, at least, they are usually free and as close as the surrounding nature-strips) so that you end up with something worth having after investing time and/or money in getting it up to scratch. However if you want to fix the one you have, just out of sheer cussedness, there is a fairly good chance that you can get a reasonable result with a new piston and rings. I'm not denying the legitimacy of cussedness: when my father died he had left a non-running 1960s Supaswift with a Villiers engine under his house, and for no sensible reason I repaired it (new rings, second-hand magneto, and rebushed the throttle butterfly in the inlet manifold). Even more foolishly I then used the horrible thing as my one and only lawnmower for a dozen years or so. OK, so it would invariably start first hit of the impulse starter even after months in the shed, but I doubt it had much more than 1.5 hp, and being a 2-stroke I often had to clean the spark plug. Fortunately the replacement magneto finally packed up last year and I had an excuse to junk the machine and buy a beautiful 1976 Victa 4 stroke, which has improved my quality of life immeasurably.
I think you will have to replace the piston in the old Tecumseh if it has broken, stuck rings. I've been known to resuscitate car pistons with those problems by cleaning the ring-grooves on a lathe then fitting spacers beside the compression rings, but it isn't worth the effort for a lawnmower, and anyway 2-stroke rings are usually pinned to keep them from rotating, which stymies the idea of cleaning the grooves on a lathe. Since your piston is also scored, which matters on a 2 stroke, a new (or at least better) piston seems essential. If you are going for a new piston you should consider having the cylinder bore honed if it can be done cheaply. Overall though, I can't understand why you would want to do these things. I had that awful Villiers thing recently enough to still abhor its memory, and I'd expect a Tecumseh to be worse. (I had a 4-stroke Tecumseh for a decade or so, and that was definitely worse.)
