Interesting things to play with.
Patents describe the item without giving too much away so often the info you need isnt there, that said the diagram in the patent shows the screen being driven via serial, that being the case it will be a very high speed serial lonk, and possibly not standard Rs232.
I'd be taking the monitor apart and looking for something that is a video input, theres a good chance somewhere there will be, unless its pure digital. Try looking at all the Ic's in the monitor and googling for the datasheets, that will give you some idea, one of them may be a video processor or something.
As for the remote, you could either try connecting up a cheap saleae logic analyser after sussing out the power connections, or just bypass all the electronics and connect everything direct.
A quicker way might be to make a standard vga/video monitor fit, you can set one up to use only part of the screen if required.