Electrical/ground seems odd, especially if existing grounds are intact. I will guess you could loosen up the throttle cable clamp(s) and/or disconnect and see if the engine will fire up? Maybe a No Start with the cable unbolted would seem to indicate an incorrect ground via the cable/clamps. If that happens, I'd refit the correct ground(s). If she otherwise starts/stops okay with the cable loose, seems unlikely it's getting electrically hot...
That said, a throttle cable is lousy conductor, and it has been my experience an unintended conductor would get REALLY sparky/cherry red hot otherwise, e.g., smoke/spark/flames, not just melty cable jacket. Maybe when you replaced the cable it got routed incorrectly, and is either electrically arcing somewhere intermittently, or is now incorrectly near a warm/hot spot on the engine.
With luck, the MTF guys will have some hands-on with your same model and can give some insight; I used to hang out there professionally during my time with Honda (trivia: Honda used to sell a 22hp diesel tractor here in the USA) and they are as solid a crew as you'll find here. Wait. That didn't come out right. (
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