If they really bill at ~$100/hr, they should certainly be comfortable with paying $50/hr to subcontractors, maybe more. (It's common to double a subcontractor's rate and bill that to the client.) So definitely don't take anything under $50.

Asking for $55 and being ready to take $50 doesn't seem crazy at all to me, but since you don't care too much whether you get it but also don't want to burn a bridge, ask for a daring "wow, it makes it worth it!" but inoffensive figure. Given their margins, I'd say that's $65-75/hr.