What scares me about these laws, is who actually carries this kind of proof? If I were stopped in Arizona (where I’m currently living), and proof of legal residency was required, I’d be screwed. All I have is a Texas driver’s license, some credit and insurance cards. It could take me several days to get my hands on my birth certificate (which isn’t original) or my DD214 which I’m gathering is what it would take to prove that I was born in the USA.
In a sane world we would expect law enforcement to use professional discretion to decide when to act. But when experience and common sense - otherwise known as profiling - are eliminated from the process of evaluation the rest becomes a farce.
I think what you carry would be more than adequate, unless you were exhibiting behavior that raised suspicion that you might be in the US illegally.