This morning I swept the floor, prepared my mop bucket, and grabbed the mop to find out the sponge part was ripping off once it landed in the water. I think I only get about three or four moppings in before that happens. Used to last a lot longer.
When I was younger, and it was easier to get up and down, I used to get on my hands and knees and wash the kitchen floor with a rag. Then I graduated to a sponge mop. I wasn't happy with the end result, so I tried the Swiffer wet mop. Not real thrilled with that either. In order to get the floor as clean as I like it, I have to go over it a couple, sometimes three times, rinsing and rinsing. So I'm basically where you are. Mopless. I wish there were a product that I liked.