There's nothing definitive published because it's all subjective, as has been stated. Look at it this way - any force that forces the BB sideways isn't going into moving your bike forward anyway - it's the use of superposition of forces when looking at a structure. I used to have a link that showed it, but can't find it now. There are basically three energy losses in riding a bike - aerodynamic drag, rolling resistance of the tires, and drivetrain friction. Since the frame (any material) flexes within the elastic range of the material, there is essentially no loss. Maybe in a sprint there could be losses from chain rub, tire scrub, etc, but they are secondary effects, not loss from the frame flexing.

A few years ago, one of the British cycling mags published an article claiming to have quantified the losses between a modern CF bike and a 1983 Pinarello. There were so many errors I found when I read it that their conclusions can be disproved.

Good luck in your search for something - I doubt anybody has published a reliable, scientific paper showing any correlation between stiffness and efficiency.,