Your going to have to forgive me, it’s been something like 10 years since I last read the play and my memory is a bit fuzzy, but I would like to help.
First, IIRC the stairs are important to the show, and the house is eccentric in character. The set is about showing how oddball the family is even though they are wealthy (am I remembering that right?).
So first, I would make the stairs a focal point.* The logistics of actually building them become a problem that you can design the rest of the set around. Stairs are a great thing to block around. You can bend them off to one wing and have another set of stairs leading back down into the offstage wing. That’s the easy bit. If you have a deep enough stage you can layer the flats to help with this so you don’t have a big swoop.
I am having trouble communicating this with words, I keep wanting to sketch for you.
I found this photo with google that gives you the basic idea of what I had in mind.
I don’t care for some of the other elements of that set, but I think the setup of the stairs could easily be stolen and used. And it wouldn’t be difficult to build. Something that is particularly important if you are using student labor.
*actually, first I would talk to the director and see what they want to do, but after that I would say make the stairs a focal point.