We're having to go to Plan B: Call the insurance company. The plumbers came back today (after I was already in Indiana) and the suggestion was to not use the pressure jet on the pipe to clear it out. There was too much chance of it backwashing into the bad section under the sink. Their office said it would be better too just replace the pipe as there was no way to tell how badly damaged it all was. There is a very good chance that it could be totally corroded and all that's holding it together is mud.
So now it's time to invoke the homeowner's policy. I have damage to the wall in the basement, there is mold where it has leaked before, and there will be a lot of repairs to fix what was torn up to replace the pipe. This is one of the reasons I have insurance, taking care of stuff when it starts to spiral out of control. I don't want to have to use it, but I don't have any choice any more.