Not a thing can be done about the available space. I suspect such garage laundry rooms were thought of by architects that never do laundry.

What I would do is raise the hanging rack as high as possible; the bar will still be about 10" lower than the top. Put a fold out laundry table with the top set at 30" to 36" above the floor. This is a Small Version. When lowered it's out of the way of hanging clothes, but you can lift it for folding towels, jeans, etc. You can buy or make one. When closed the support swings sideways against the wall and the top drops over the support. Larger versions might need two supports, and metal Folding Shelf Brackets can be purchased.