In case this is useful to anyone, there's lots of digitised newspapers freely available in the Library of Congress: https://chroniclingamerica.loc.gov/
Chronicling America is great, but as you’ve noticed it’s limited to issues that are in the public domain. It’s not just LC, the National Digital Newspaper Program[1] has been funding hundreds of libraries across all 50 USA states to make it possible since the mid-00s.
Australia’s national library offers Trove[2], which has a huge collection of Australian public domain newspapers.
Most of their repository is likely funded by your tax dollars and is there for the public to use.
Trove is fantastic. It came in handy very recently for the same project I used the Library of Congress for[1]. The Museums of History New South Wales has a great online archive as well[2].