Just like you mentioned, you would be seated in the quinjet and then drop out. Going off of what Marini said shortly after it was announced, I think what they were planning is have each "Quinjet" be on a rotating carousel ala Falcon for capacity. There probably would've been an animatronic of Black Panther "piloting" the Quinjet up above. Something would happen, maybe a missile would crash through the Quinjet like StormChaser at TDL and we would have to evacuate. Now here is where the FoP part would kick in:
Like you mentioned, the seats would drop out, perhaps get spaced out to make a more intimate experience, but they would probably do so quickly to add thrill, and they would drop in a reverse manner of Soarin'. In other words, like how the gliders in Soarin' move above each other with the furthest back going the highest, it would be in reverse order; the front row would drop below the first row. Add in a blast of fog to help cover the transition and now it's FoP. We have our own "dome" on the carousel.
Now here's the kicker: it wouldn't make much sense story-wise to have us back on the jets if "something goes wrong" in there. We would probably have to rotate into a different chamber to exit. Maybe it would be next to the Quinjet we got "blasted" out of. IDK. That would probably be a hassle dealing with the guests' belongings.
But yeah, that would explain why the show building looked REALLY tall in the concept art. Gotta make room for the "Quinjets" towards the ceiling and the big screens beneath.