Re: "the brainchild of Airborne Systems of New Jersey"
NASA's early 60s projects were Rogollo wings (which evolved into hang gliders and delta kites) and were for the Dyna-soar project, not Mercury/Gemini.
Dyna-soar was part of the manned space plans which included the Sea Dragon launcher (600 feet long, built from 8mm submarine steel in a shipyard, 100% reusable, no turbopumps (engine pressurisation via liquid nitrogen boiloff). The engine bell of the launcher would have been large enough to completely cover a Saturn V first stage)
Stunt kites (actually power kites, only the smaller ones are stunt models. Anything bigger than 1.8 metres simply can't manouevre quickly) are a derivation of parafoils, not the other way around.
I built a few Rogollo wings as a teenager when interested in kites. The advantage over Deltas was that having no rigid spars meant they were easily compactable (useful in a returning capsule) - but that also meant they were susceptable to crosswind gusts collapsing them at inopportune moments when close to the ground - not the greatest thing to happen when carrying a manned capsule, and that's why normal parachutes + water landings were used throughout the US manned programs. I did build one with inflatable spar pockets and it worked very well, but having something like that would be far too risky for spaceflight (if the pockets didn't inflate you're back to the same problem as before).