RE: Looking for help... propeller sizing
A thought based on past experience working with naval aircraft. (ie.. carrier take offs)
A catapult would most likely be out of the question not only due to logistics but stress on the airframe would be tremendous but a blast deflector at the beggining of the runway would give your prop wash something to push against and may help get you up to speed faster.
Just a thought, it would be interesting to see how much difference it would make?