think L/D relates with hang time once airborne
L/D affects everything. L/D affects hangtime, more L/D means more time in the air, more L/D means when you are in the air you have more speed, L/D will also tell you what the top speed of the kite is that is how many times the windspeed you can go, L/D tells you how good the kite goes upwind.
Now, L/D is not just a number but a function. Most C kites will sit deeper in the wind window and because of this they have a higher angle of attack and this gives them more drag than a bridled kite, which presents a smaller angle of attack to the wind and goes upwind better. But this does not mean that if you forced that bridled kite deep into the power zone it would have a better L/D ratio for that angle of attack, and this is why even though it seems like C kites have more drag than bow kites, what you are measuring is not the same thing you are measuring the L/D at different angles. And when you jump, you will put both the C and the bow kite at about the same angle of attack.
Here's a chart of a propeller airplane, it's not a kite but it shows you how as the angle of attack changes the drag keeps increasing, until at 90 degrees drag is 100%
So yeah, I think L/D is key to the highest jumping kites, but not a static L/D for the kite overhead at 0 degrees as it is usually measured, but the entire L/D function, from 0 to 90 degrees.
As to which kites have this particular characteristic of a great L/D through the entire range of angle of attack used in a typical jump, hard to say, but the most efficient kite will waste the least energy and jump the highest.
Talking about wasted energy . . . If you megaloop your kite, to get that great sideways yank you have to start looping the kite before you are all the way at the top of the jump. Then when the kite goes through the power zone, you get 100% drag, and a big yank, that's the megaloop, then the kite goes overhead and catches you. But this big fat megaloop also means you jump lower. If instead of megalooping on the way up, you wait until after you are all the way at the apex of your jump and then try to kiteloop, you will have already converted most of the energy of the wind into height and instead of a big sideways yank, you will get a gentle kiteloop on the way down, more of a helicopter than a slamming sideways yank. This is also why a kiteloop on the way down is so much more gentle than a kiteloop on the way up. On the way down you have already used up the energy of the wind.
You can either use the energy of the wind for height or you can waste the energy on a kiteloop for a sideways yank, or you can split the difference and put some into height and some into a big sideways yank, but you can't do both there is only so much energy in the wind. Any energy of the wind you waste on drag can't be used for height.