As a new kitesurfer (just did my first jumps last night) I am interested in the explanation of what "pop" is and how it affects a jump to begin with..... as long as the rail is stiff enough to hold a good edge prior to the jump, it really doesn't matter just exactly how stiff it is... I think probably 99% of your boost comes from the kite/lines and your own legs. But, I'll happily accept any explanation as to why I am wrong.
You lost my attention in your scientific diving analogies, but think of it this way...
Some jumps are just achieved by sending the kite correctly. You don't even need to be on a board to go up. You can do it running on land.
Some jumps are achieved by keeping the kite parked and popping off the water. Loading up your edge, not doing anything with the kite. Think of a snowboard jump/pop when you aren't hitting a feature, but are just moving along and can pop off the flat.
Some jumps combine both and you go huge.
Flexible boards are nice to ride in chop. It is like cruising with a pair of Nike Air running shoes. They absorb all the crud so you get a nice easy ride. However, when you jump, some of the energy that you load into the tips of the board is going to be lost in the board flex. A stiff board will transfer the most energy from its press against the water's surface to your big air release.
There's a lot more science to it than that and you want some combination of flex and stiffness so you can load up the board but also ride comfortable.
Maybe that helps? Maybe not. It is also very possible I'm talking out my ass...
Have fun and welcome to the stoke!