The website was giving me the wrong zips, too, in the past. Forum members told me they were wrong but, the website was saying something else. So, I started using this site. [www.easypost.com]
and found out the forum members were right.
If you really want to do those USPS Hazmat shops, just mail the package to the Food Bank in zone 5 -- just like we did the old dim-wgt USPS shops.