Can you look at past years to get an idea of if the child faces this "overload" thing year after year? My guess would be that many kids do move into the district, and it would be unusual to be bounced year after year.
Reason I'm asking, is, that depending on the kid, and you know yours best, being bounced around for one year in 2nd grade for two months or less, wouldn't be more than a temporary inconviences. I think the kids are young enough that they follow the teacher's lead. For my own son, changing schools every few weeks would have been fine, if it was explained to him upfront that it was going to happen, and why.
That last chance to switch to the neighborhood school sounds both appealing and scary. One one hand, being offered a spot in the room of the least wanted teacher isn't appealing, on the other hand, being able to leave a bad situation without penalty is appealing. Too bad they won't cluster the "skippers" together as they travel from school to school.
Smiles,
Trinity