Hi Debra,
I don't blame you for not wanting to file the tertiary claims. They are a real pain. I think that if the tertiary company is a company that you participate with then you are required to file the claims. Usually it is in your contract that you must file all claims. I would check with your provider rep for BCBS or another insurance carrier to see if they require it. Hopefully, you're only looking at a few!
Good luck
Michele