Hang a chest rig on the back of the seat, add a molle butt bucket at the bottom, and an elastic loop with a hook on one side to the top. “Drawing” an AR from a completely enclosed case/holster on the back of the seat isn’t going to work, and a side entry zipped case isn’t going to be very quick to access.
An Eberlestock rifle case hung on the back could work quite nicely too, but again, the more enclosed the bucket, the harder it will be to draw the rifle for use.