What qualifies as proof of residency for AML in the USA?
There is not. You will not find a definitive list of allowable documents, endorsed by a government, regulatory body, trade group etc. You may find lists of generally accepted documents, however there is no guarantee that their acceptance is either uniform or universal. 

Documents typically considered acceptable for the purposes of establishing residency at a given dress i.e. rental agreements, mortgage documentation and utility bills (such as gas, electric, water) are generally utilized (and accepted) by the financial institution as they tie the individual directly to the address thereby satisfying elements of AML/CFT, specifically the Know Your Customer and Customer Identification Programs. 

Your only option is to await a response from the specific institution (in this case exchange) and inquire as to what documents they will accept in lieu of the aforementioned, if you are unable to provide them.