For which grade?

Why did you sign a lease that starts August 31 and not August 1st OP? That seems very weird. Contact the school but, if relying on being in-boundary for enrollment, unless you can clear a home visit, be prepared to potentially miss the first week of school and start after Labor Day.

Where are you living before that? You do not really need to prove you are inbounds since there is a "homeless" loop hole for registering. As you note, schools would rather know who is attending earlier rather than later.

Call the school and ask.

Any idea what we should do if we have an Aug 31 lease start? If we have the signed lease, is that enough to prove we will be in bounds or do we need to attend our current school until our lease starts? Seems like this would be a headache for both schools!