Really reluctant to get into this because you have an expert on scene telling you what his expertise and testing say. But still, this is a Forum:
1. 100% behind the idea of carb trouble. Technically a "replace as assembly" item but some have had luck with repairs. The Stuck Throttle idea intrigues me and makes sense. If shop labor's involved, cheaper and more certain to simply replace.
2. Those logic boards fail pretty often. I think allowing the genset to cool a little by running unloaded before shutting down might help preserve them. Dinosaur replacements are supposed to last longer than OEM. Hope your shop consideres those. Flight Systems has some parts too, but I don't know about your model.
3. A Stator Rotor has lots of ways to go bad. Dirty slip rings doesn't mean BAD, though. The failure I've heard most about is from sitting so long that the laminated steel parts rusted and swelled. Then the rotor can't, well, rotate. Those few months don't sound long enough for that to happen if it ran last winter.