Nerdy library swindle- gotta fake having a certain address on a piece of postmarked mail, to get library card for the GOOD county near mine!

I cannot survive without the library. The rich people county I moved from requires I submit new proof I live there every 3 years. I figure fake IDs are a bit hard, all I need is a piece of postmarked mail to prove I live in the county next to mine. I moved 1 mile from the border into that county, and am now in a super awful library district, so I must renew my old card and fool the librarian. What's the best way to get my name + old address on a piece of recently postmarked mail? Alternatively, I could get a lease agreement as proof of residency, but that one may be trickier to forge.