If you make a tread deeper, it will just stick out over the tread below it. We had similar basement stairs (steep and shallow) and just pulled them out and put deeper, less steep ones in. We don't have room for a landing at the top or bottom now, but it is worth it to have stairs I am not scared for the kids to use.
My personal preference for safety reasons is not to have carpeted stairs. They just seem too slippery for me, and when the carpet gets worn at the nose it is too easy to slide off if you step wrong.