I would go with option 1. I don't see a downside, unless you want to eventually show 1/2 of the split screen taking up the entire screen without losing resolution. If that is what you want, then I don't know.
Can you describe the scene/application for the shot?
If you are trying to do a Woody Allen Annie Hall sort of thing, you need to shoot what is called an "indifferent static line". This line is often an object in the room that is vertical so you have an easy time matching up the frames in post.
Yeah just film the two scenes as normal and split it in post. Seems like a sound idea... Thats if I understand what your after that is.
If you need timing to sync if you have access to another camera just film the scene with both and then split in post...
Or just film it one at a time and make sure the second actor is reacting to theprerecorderd other actors lines. If its a telephone convasation type shot.