I really don't know if it's possible to generate a proper 1-bit video signal with a TI 84+, but I ran some tests and this is my best result:
It alternates the linkports' state rapidly, but it's still too slow to generate a full white screen. I used AXE, but I think I have to use very optimized ASM to generate better video. Even then it won't be possible to do anything else but video playback.