Clearly you don't want the body frontal area to be any larger than the largest thing in the bike. What's the biggest thing? The engine or you? Feet first would seem to have some aerodynamic advantages in a narrower front end. (At least, my shoulders are wider than my feet.)
Something I have not seen mentioned too much as regards the 'flat on your back' riding position is that, if you are the biggest thing (vs the engine), you need to be as flat as possible. Well, if you are laying flat on your back, I don't think you can see forward.
2 possibilities to overcome this come to mind.
First is a periscope prism/mirror arrangement that would allow you to see forward. Jack Costella had a periscope on one of his racers - so no new ground there. You're just going to have to design it to give wide enough forward vision to meet the rules. (FWIW, Jack told me he didn't like it.)
Second possibility is a video camera and flat panel display. Some of the human powered bicycle riders are using these on their fully enclosed bikes. You'll need some lenses to adjust for the short focal length. This has not been done in LSR to my knowledge, but I did float the question a while back. Response was 'we'll have to see it', but I wasn't shut down. Proof would have to be provided that whatever system provided ample visibility and (for me at least) had an automatic fail over. (going fast, screen goes dark, uh oh).
I can't address the issue of balance while lying flat on your back, might be interesting. Seems that the human head was designed for balance with the head upright - don't know how good the physiology is for head looking straight up. Certainly the mixed signals of ears say I'm going down, eyes say I'm going forward, would be an excellent recipe for vertigo.
Claustrophobic street luge anyone?
Thanks,
Jim.