Yeah, I think mine faces west as well.
East may be ideal, but I don't think it's important enough to have to rearrange everything for it.
I never had a "corner", always a wall with table or, when in college, the top of a dresser. Sometimes West was the best I could do, other times Southeastish, but the majority of the time East worked out.
But for us, East is actually more important than facing the icon, so our piety would not see anything odd about praying toward the East even with the icons on a Northern, Southern, or even Western wall. Personally, I never managed to choose East over icon of my own volition, but I've been in such a position many times before.