I think that I'm probably going to just let her do what she wants as well. There's now another one of my hens that actually ACTS a bit broody (feathers ruffled, pecks at you, that sort of thing) and she's now hanging out with the other one in the coop nesting box. No egg production from either one of them.
We are new to all of this as of April so perhaps they just have to let this sort of thing get out of their systems. We had one chicken that was broody a couple of months ago and setting on 15 eggs (which weren't fertile as no rooster around) - so that was easy to deal with as we just put fertilized eggs under her - but, these girls that aren't laying and are just hanging out in the nest boxes - they are just a bit more difficult to figure out.
Sounds like you went to a lot of work building a broody cage - not sure I want to go to the trouble as I'm pretty sure the rest of the gang will do just what yours did. Maybe mine'll get over it as well - I hope so.
