New wrinkle. The boys' elementary school has a skating party once a month. Got home from said skating party last night, open the garage door and see a large puddle (the laundry room is in a room in the back of the garage). Get in the house and see the utility tub full of water and towels all over the floor. Boys are a sweaty mess from skating so I tell them to take showers, but to make them quick, while I keep an eye on the water level in the utility tub. That's odd, between their showers and mine, not only did the water not go up, it seemed to be going down. Before I left for work this morning, I turned on the water in the now empty utility tub for a bit. Only took a minute or two before water was backing up. So, even though our main is not good, it was working good enough. Apparently the problem is actually in the utility tub somewhere. I checked the trap, but I guess some more disassembly is in order.