I must say, I dont think anyone of you are right here
I have no facts (yet) about this, but the stored energy in the board would be almost nothing at all IMO, so a too soft and too stiff versus a medium soft board, does not contribute to "energy" in any significant level whatsoever IMO.
I think (I dont know exactly, I admit, just my intuition and experience) that the difference is purely the dynamics of "correct" flex for a given board in given conditions (and maybe for a given rider too), will allow you to make the most efficient pop that gives you the best release and takeoff
So just as with kites and waveboards and everything else almost - I think it is the overall combination of physics and dynamics that is essential for giving the best (individual) board, so not about stored energy really, but all about getting a clean harmonic dynamic feel in the board, when you load and release
Just my thoughts...
PS: I think I know exactly what you "miss" in TT's now you've become a directional addict !
I got it the same way, and had to move to a bit wider and more flat TT that went higher upwind and going early, as it felt useless to just go back and fourth with a "mini" board in order to make ONE huge jump, and then back and fourth again....
But I found, that going for more voluminous TT's were not the way - simply choosing some that went a bit better upwind (flatter, wider, straighter lines), was my "new" solution.
Personal taste, I know - as of course a more curved board feels way more "directional" like and smooth, in tight carves - but on the other hand, you GOT a directional for that - so what you miss on your TT is most likely the ability to go upwind really well ? (or just me ?)