The squirrel has just left the building.
We had called a few places, but didn't get anywhere. Willamette Wildlife Rehabilitation (who do great and important work, but really, thinking my husband was going to set the squirrel on fire was ridiculous) couldn't help, it's not what they do exactly, but turns out we found a fantastic pest removal guy. So I'm giving him a free plug.
Ellis Wildlife Removal in Alvadore, Oregon. If you find yourself in need of this service and are in the Eugene/Junction City area, use him.
We had to take apart our fireplace; remove the bricks, take off the metal, etc. We have a sooty mess with an unusable fireplace, but thankfully we aren't in need of the fireplace and the mess is nothing. The squirrel is safe; alive and relocated.