I was thinking more 2-player simul since there won't be any 3D stuff. Your two characters would be in the center-bottm, just background tiles. They're behind something, and when you push the footpedal they jump out. Then everything that's attacking you would be firing bullets down towards your "area" and if you don't let up you see yourself getting hit. No scrolling necessary.
I don't think it would be twice the time would it? Starting with half the screen just eliminates the first binary check.
I was thinking more of a 2-player coop with shared screen though so you could play one-player-two-fisted
Another way to cut down on the time needed is to only have enemies show up in specific spots. If there are only 16 places an enemy could appear in on each screen, that only takes 4 checks to complete, and then you wouldn't have the entire screen turning white/black for that fraction of a second (which I still think would be very jarring) and would get no tunnel effect.
We could simulate the 3D "ducking and hiding" if we just have the whole scene scroll up really fast when you duck, and the background below the screen is of barrels or whatever. Might be kind of dippy though. Also I'm trying to keep this concept simple, and scrolling simply isn't.