Today has been quite an interesting day!
I called another plumber to get a second opinion on the bathroom repairs. They came out, took out the toilet, & cut a hole in the drywall to survey the situation. $170 just for that. Turns out it's a cracked drainage pipe in the wall. Another $460 to repair it.
In the meantime, another company came out to set up dehydrators & fans to dry out the water that has seeped into the walls & under the linoleum. They said the fans will have to stay there for three or fours days before it's all dried out. I have no idea how much they're going to charge for that, but it sounds like it will be hundreds of dollars.
Then the insurance adjuster came to the house. He took photos & worked up an estimate for the repairs, as well as the replacement of the tile, drywall, carpet, shower, etc. They estimate that it will cost between $5400 & $7700 - not including the dry-out service - to complete all the work & put my bathroom back in working order. The good news is that they are going to pay for everything minus my $500 deductible.
The only thing that still worries me about this whole thing is: How much will my insurance premium go up after this?