When one of my children miscarried, I conditionally baptized him/her (too small to tell) because there was a chance he still lived but absolutely certain that in a short time he wouldn’t be. Still, I would not violate canon law by presuming to baptize any future child who is not in immediate danger of death. (violation of canon law - at least when one is aware of it - is a sin)
It does not seem at all likely that I would ever be in a situation where any priest would be totally unavailable so I don’t have any plan in place should that occur.
It is unfortunate your parish is so limiting. Mine will baptize at any Sunday Mass. Parish size sometimes makes a difference, however.