Let me ask, was part of the $1000 used for the prebuy inspections? Seems like you're getting screwed. I'd probably ask an attorney but you should be able to send him a demand letter stating either complete the paperwork and put up the purchase price by x date or the deal is off and there will not be any further refund of the deposit. What's the point of a deposit if he can force you to forgo a sale to someone else indefinitely and then get his money back?
He should have sent you a signed copy of the purchase contract before you signed it. Without reading the actual contract, it would seem that since you signed it already, he can prevent you from selling the airplane because if you did, he can then sign the contract you returned to him and claim you had already sold the airplane to him.
Good luck getting this sorted out. I'm hoping the buyer is a stand-up guy and completes the paperwork and sends you your money. You might have to get some legal advice if he continues to stall.