I would have done address line 1, address line 2, line3, etc. I think people got confused by your form because they are used to typing in 1234 Sample Street <tab> expecting to be asked the rest of the information further down. The other option would be on form submit to show what they have put in and say "make sure this is your full address [CONTINUE] [EDIT ADDRESS]."
Really, I am no legal expert but I did once sue someone in small claims court. They wanted to know what I did to verify the other party's address, not just taking their word for it.
The only case where I've seen address used as a disambiguator is when treating multiple private individuals with the same name, but in that case also you want some official ID, not the address which may change frequently (and may contain a different John Smith than the one who lived there a year ago).
We need a name for this.