I'm planning on solid 3/4" prefinished hardwood (red oak) to my living room/den. It is 3 steps up from the next room and 14' wide x 24' long. The problem is that the stairs to the living room come in parallel to the joists. If I lay the floor out perpendicular to the joists I won't be able to leave a expansion gap at the top of the stairs. (ends of the flooring would butt the top of the stairs)

How should I approach this?

Appearance-wise it would look best if the boards were laid perpendicular to the joists (like they should be). The subfloor is 3/4" plywood, 30# tar paper, then 1/2" plywood on top of that.

You would be alright I think to butt that if you leave a little on the opposite end. Solid wood does not move much if any on the board length. It is the board width where you really need some expansion.