Do you have a shower or a bathtub? I have a bathtub. Like you, I live in an apartment with an inefficient dryer. I don't have any outdoor space.
I place my laundry on hangers and hang them from the bathtub curtain rod. I also bought another curtain rod and hang that over the middle of the tub. I'm short, so the middle rod doesn't bother me and can be left in place. Obviously adjust for your height. With two rods, I can hang a full load.