I think I figured it out. The url amazon gives you is just
https://www.amazon.com/update_Kindle_Paperwhite_7th_Gen, but I put it into jdownloader2 and was able to figure out that the actual file it links to is "https://s3.amazonaws.com/firmwaredownloads/update_kindle_all_new_paperwhite_[VERSION_NUMBER].bin. So I put in
https://s3.amazonaws.com/firmwaredow...te_5.9.6.1.bin and got the older firmware file, hope that's the right thing.