I still think you need to go back to first principles.
POSITION of the rider.
Fashioning handlebars that will allow the rider to lay flat, back horizontal, feet on the pegs, hands close together (like a praying position) will give you more aero benefit than a fairing.
Why would you streamline a barn door?
The front wheel would be an additional opportunity - but secondary to position. KISS - Keep It Simple Stupid - should be the goal along with low drag.
Rollin Free (?) had it figured out long ago - but that was really extreme.
Good luck on your venture.
Thanks for your encouragement, MAYO', and please believe I am not disagreeing with you.
This particular project started with an existing bike, an existing engine, and an existing rider. It was my job to cobble them all together into a safe entry that would pass tech. Trust me, we KNOW we're far from optimal for LSR. The best-but-joking advice I got was in an email "make your rider smaller" but alas we can not. This adventure is all about my good friend hearing those magical words "the course is yours."
In his full leathers, and Snell helmet, and considering he has to keep his feet on the pedals, Jimmy can lean forward only a bit, nothing like a regular bicycle tuck, and the adjustments accommodate that. If you're having a hard time picturing our limitations, put your full USFRA motorcycle gear on, and then try to handle your pursuit bicycle.
All of this is exactly why I asked the question... considering how inefficient our bike and rider position is, would a fairing help? Now I know the answer is no, and I'm good with that. Jimmy will still have fun, and I still get to try to tune for top speed. Nobody loses with this endeavor.
If ever I find myself in a position to build a 50cc LSR bicycle from scratch, well, everything you say would apply, plus I'd start with a skinny little rider who practices yoga. I don't know, but maybe that's you?