That's the funny thing about behind the neck work. Back in the day, like in the '50s and '60s, that was pretty much the go-to for big pressing. Whether it was more popular because people already had healthy shoulders or if it contributed to shoulder health, or a little of each, is interesting.
One thing I like to do with BTN presses is to setup the bar in a rack like usual, around shoulder-height, set my hands in a pressing position and duck in front of the bar, then quarter squat down until the bar's about eye-level (behind my head) before taking it out of the rack. Then stand up while keeping the bar at that same level, so you can start the press with some tension in a more powerful position, compared to starting the first rep with the bar on your traps.
Depending on the seated rack setup, you may be able to sit facing the seat, so your back isn't supported at all.