I would let the tree die before I'd let someone come into the yard and spray poison. Seriously. Once they're in those little cases they're fairly impermeable.
There isn't much in the Organic Library about
dormant oil, but I just looked up
bag worms and learned something new. It looks like Bt is used on them this time of year (makes sense - if the mouth parts come out of the case to eat, you can get them that way). But Bt shouldn't be broadcast all over because it will kill butterflies. I think the "spring" for dormant oil is probably past because it's too warm now. If you pick up a bottle of Thuricide and mix it into a spray can with water and you might want to add nutrients like fish fertilizer or liquid molasses) you could treat and see if that slows them at all. Don't spray on a windy day and be careful just to hit the plants in question. It doesn't take much Bt, and keep the bottle in the fridge.