UPDATE: April 22 What I ended up doing was removing the trim non-destructively. Above the door frame, it was clearly not load bearing, so I continued and was not so non-destructive. The end-result are doorways that are standard height (and I can walk through them without ducking)
The 3 door frames on my second floor are 6 ft tall. Myself, being a hair over 6 ft tall, often hit my head. Our ceilings are also 7 ft tall, and we have sloped ceilings upstairs, so it already feels cramped
We don't have doors upstairs right now anyway. Instead of getting custom height doors, I'd prefer to increase the height of the frame and use standard size prehungs.
How can I safely do this (or determine that it will be safe to do this)? I don't know how to determine if these frames help with load-bearing. My guess would be the remove the trim, cut away the plaster above the door, remove the cross piece of the frame and nail another one into the top-plate of the wall. What I'd hate to do (or whatever, what my wife will yell at me for doing) is destroying part of the wall and frame, and finding out I can't do it.