If you don't get any water in your basement except when the drain backs up, why not plug the drain and carpet over it. Install a laundry sink in the laundry, and any backup will go into the sink (assuming that is the lowest drain in your house). A plastic laundry sink is cheap, and easy to clean (disinfect) if you ever get a backup. Also, your choices for carpeting are either glue down or simply laying it down because stretching it will probably create a gap at the center of the basement floor because it is sloped such that water runs to the drain. How about using carpet tiles that could be glued down and replaced individually if need be. Good luck.