Update - brought home 3 options from the hardware store and none worked. What appears to be foam insulation in the wall is preventing the anchor wings from opening in the wall. And the self screwing anchor wouldn't work either because the hole in the wall is larger than the head on the anchor so it comes right back out of the hole. At this point I'm thinking the only hopeful solution is to glue a slice of 3.4" diameter wood dowel in the hole, let it dry, then drill a pilot hole and hope it will hold the cord tensioner spool in place. Good news was I didn't need to restring the shade; when I removed the bottom rail I was lucky enough to find the missing cord end was inside the rail and not broken!
