I returned with a huge roll of far more heavy-duty plastic sheeting than we'd need, and the largest size wet/dry vac Home Depot carries.
With these tools in hand, side by side, Lut and I battled against the forces of watery doom.
At first, I thought water was winning. The carpet was, and is, soaking up more water almost as fast as I can vaccuum it up.
But the rain has all but stopped, and less water seems to be coming in from the two main leaking areas. Lut thinks the vast majority of the water was coming from the flooded extension, and he may be right. I know that at least a couple of spots in the area where I sealed are leaking, but it's not clear that a lot more water is coming in through this area.
Anyway, our efforts seemed to be reaching a point of diminishing returns. We shifted to higher ground what we could shift, put sheeting under what we could wedge it under (at least the futon frame should survive in good condition), and vaccuumed or swept into the sump pump thirty or more gallons of water. Before bed, I'll tackle the extension again, since if that's the source it's best to get it there.
Then ... we'll see. I gotta figure out where I put those phone numbers for foundation specialists.