The OP actually posted this same document in Post #12 which provides an answer to his original problem. Plus it gives him even more features. Talk about hiding in plain site.

Now the question is what types of (spare) cables does he have running from processor to projector? He just needs to make up a null modem cable. If he has a spare Cat he can make RS-232 adapters* with the proper pinout configuration.

*Ernie: Note the word "Adapter" and not "Balun"!