@maxdancona,
Max I was in a simular position with my daughters when they were young. I made sure to talk directly to the principals of th school involved as well as anyone at the school board offices, and the district offices. I went always in person and hand delievered everything. I stayed cheerful but concerned and I carried a large novel of I couldn't get an appointment and I told them I understood they were busy but that I knew that if they could squeeze me in at a random moments and I let them know I would wait all day and I was grateful for their help.
If nothing helps (you do still have most of month to do these things), you still get your daughter into that other school because busing is mandatory and its worth the effort to give her a step up.
As a single dad doing those things and letting them know I would move heaven and earth while remaining in good humor - both my daughters went 3.5 or better through public schools at the best we could find and they got scholarships (St Edwards University and Texas A&M) and both graduated Summa Cum Laude and working in their fields having had job offers prior to graduation.
It can be done. Don't miss deadlines, hand deliver, be pleasantly insistent on face to face meetings, and good naturedly be insistent and make sure all principals, Councillors, teachers know you by sight. Do not miss appointments.
There is absolutely no way a lawyer can help you with any of this except to advise.