Frame a door under or around a beam?
Cutting a door isn't hard: clamp a straightedge to the door and go at it with a circular saw.
If you wanted to maximize height, you could use the beam as the head of the jamb. Maybe skin it with 1/4&quot; luan to hide the rough lumber. That would leave you a 79-1/4&quot; height, which is probably indistinguishable from a normal door.
That said, however, your adopted code might actually specify 80&quot; height for egress, so you need to decide where you stand on that sort of thing.