Thanks for all your replies, including the Floormate tangent -- I may have to get one of those, too.
Well, I ended up buying the Swiffer with the $7 off coupon. I just finished its inaugural run (My life must be really exciting -- it's 9 p.m. on Friday night, and I just finished mopping!) I started by doing the powder room. It worked like a charm and I was finished in about 5 minutes.
Kitchen was not as successful. It was faster than my regular mopping and I wasn't drenched in sweat when I finished, but it's not as clean. I think it might work, though, if I do it frequently enough. The floor was probably dirtier than a Swiffer can handle. I said I wanted this thing to clean inbetween regular moppings, so what did I do? I used it when the floor was good and dirty.
I did really like that the floor wasn't sopping wet. I towel dried my floor before, and it's not at all necessary with the Swiffer.
I did use three cleaning pads, so that can run into some expense. The mopping solution, though, is no more expensive (my be less) than what I've been using.