When I saw your Hummer pictures, the first thought came to my mind was, Oh, no, they are NOT going to total that Hummer. I don't know how you can fight the insurance company on this, but time to put on that thinking hat and no more Mr. Niceguy. 4 months in the shop, minimum plus, you make monthly payments, and it wasn't even your fault. Better make sure it doesn't get on your driving record, it happens. Keep record of everything. Ask and demand, they can always say NO. You got nothing to lose. Good luck.
Just looking at the pictures, there maybe NO frame damage. The damages seemed to be body, bumper and glass, plus intereior damages. If the body shop discovers any frame damage, maybe that's fighting stick you can use with insurance company to demand "total".
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