Thanks to everyone who offered advice. We removed the blind from the wall (biggest job was removing / replacing the zillion cleats the RV manufacturer used) then pulled the end pieces off the bottom finger hold. That allowed us to slide off the finger hold and retrieve the string that went up inside. Reversed the process and it's as good as new.
As I said, the biggest job was removing all the valences. At least next time they'll have removable screws which will make the job a lot easier.
I'll file the advice on restringing - I'm sure I'll need it someday.
