The update:
Oh man.
So I knew it would need a new battery, new front tires, new fuel, new fuel filters.
The front tires were an all day job, longer counting finding some tires and putting them on the rim. The wheels were so fused on the axel that it took me and my sister both a long day with a gear puller, hammers, lots of work, sweat and inginuity. I couldn’t find my gear puller before I left for the trip, so I bought a new one down there. There was also a hydraulic version for $80, and I passed on that. Big mistake. It took a lot of strength and persistence and WD 40, for whatever good that did.
Tires and battery and new fuel and it started right up. But the transmission was wonky, uncontrollable forward motion. Then it couldn’t start it again.
Lubed the linkage for the HST (good tip from here), but I spent another day trying to get it running after changing the fuel filters. Finally after a long day of messing with it and troubleshooting I figured it was the lift pump — there was no fuel in the line going to the fuel pump. It would run, badly, if I squired fuel into that line and put it together, but only for a little bit. But I didn’t have a lift pump and the trucker showed up.
Sent it down to my daughter, ordered the lift pump from amazon, and found a guy near her willing to do a house call. His call was going to be just diagnosing for his first visit, but he also concluded it was the lift pump, and the amazon one had arrived, right there, so he put it in. Ran.
So my daughter can mow her lawn.
She’s going to get him back out there at some point to do more maintenance on it. For one thing, I greased the two outer zerks on the mower deck, but I didn’t manage to get in to do the middle one.
Hopefully will last her a good while.