I have a JP1 file for this projector, but I don't know how much use that would be to you. If you have an older One For All or Radio Shack remote lying around, you could use the CD/0156 code to teach your MX-700, using advanced codes which I could provide.
If you think it's worth the expense, I could sell you a remote which I would pre-program to control your BenQ.
If you think it's worth the expense, I could sell you a remote which I would pre-program to control your BenQ.