I hope the rain slows down significantly for you soon! That is quite a pond in your neighbors property! I have an auntie who lives in a very, very rural part of Oregon, and that have quite a bit of property, and it rains A LOT in OR, and the field(s) they have get so pond-like!
Forgot to add that I really like your idea of an airplane/helicopter that pumps rain water from somewhere that has too much to an area that could benefit from it!