Update:
The stock carb was stopped up as bad as I've ever seen, and 5 attempts at cleaning it up resulted in a carb swab. I went with a Mikuni VM24 which is a pretty standard swap for these little bikes. Little Girl helped strip the bike down every time and she watched and asked great questions as I figured out the particulars of changing from a dual cable throttle to a single. The bike fired right up on the first bump of the starter and Little Girl jumped around giggling.
The bike was running super duper rich and blubbery, but it was good enough for the first lesson, where the clutch engages. I want her to have fun and build positive memories around this experience, so taking small steps and stopping on a high note are very important. Last weekend she learned to release the clutch just enough to feel the bike move beneath her and then pull the clutch in quickly to keep the bike running. Success for this first lesson was doing that 5 times in a row and it took ten or twelve attempts to get the first one accomplished, but she got the hang of it and was super proud. We stopped on said high note.
Yesterday we took the bike over to her grandparents house for a 'social distance picnic'. They have a huge lot for in the city, and there is enough open space (fenced, lol) to learn lesson two: full clutch engagement. We repeated the first lesson until she was comfortable and then took the next step, getting rolling and then stopping. She killed it seven or eight times and then it happened-
She got it rolling on her own, pulled the clutch in and rolled to a stop! She was so excited she hollered and lifted her hands in victory, promptly stalling the bike and falling over while laughing hysterically. I call that a win!
We took a break to eat lunch, and then she got back on the bike. She got rolling half a dozen times and you could just see the confidence growing with every success. I had her stop when she rode all the way across the yard.
We have along way to go, but the journey is starting!