If it was my home, I would really think long and hard about cutting a joist. I would begin to think about just cutting a nice square hole, picture framing a border, and just using a step ladder.
Steve, if you cut a joists, think this out loud with me, you will of course be putting stress on that entire run, then when you climb up the stairs, you will putting more stress on that joists, then when you climb up on the attic area, you will putting more stress on that joists.
When you cut that joists, it is just there now. Its support function is absolutely gone. There is actually no way that you can support that joist unless you opt for beams in the room supporting that cut joists.
Steve, I would not do it.
Are all the ceiling joists in the home 16 oc?
I am real sorry, I thought that I fixed your problem quickly.