Rob, I will certainly agree that Shamu's cavortings above the water are ballistic like the paths of most fish jumping out of the water.
I saw a bass come out of the water vertical about 3 ft above the water and take a sparrow off a tree branch of a dead tree. Nothing left of the bird but some small feathers on the surface and a few short lived bubbles. The fish was still wagging its tail while in the air but it is not likely it helped much once he was airborne. (A new lake near Duncan, Oklahoma circa 1958-9)
Your comments about the flying fish staying close to the waves could easily be interpreted as them being in ground effect as well as riding on the uplifted air being shoved ahead of the moving wave. Pelicans are particularly adept at that. This is also practiced by some soaring plane pilots flying out of Dillingham on the Hawaiian island of Oahu.
Oh, about the birds that have to run to take off. If they were on our experimental conveyor it would cancel their forward speed relative to the earth and their running would not give them any more airspeed so they could not take off.
Pat