Next Page Buttons when wordpress is not hosted at the root

Folks:

We might have a bad setup, or we might have a separate issue and am hoping you can point us in the right direction.

We host wordpress sites behind a reverse proxy. So when someone (not us) has https://example.com/subdirectory, they try to pull the content from our site which is hosted at https://oursite.com.

Now on https://oursite.com we have WordPress installed and we have the SITE URL and the WordPress Address (URL)both set as https://example.com/subdirectory. Now we do this so that our wordpress admin is available at https://example.com/subdirectory/wp-admin so that the cookies that are set for logged in individuals is on the same domain as https://example.com/subdirectory.

When the setup is like this, unfortunately on the edit.php screen for pages – the URL behind the next page and last page buttons seems to still be using HTTP_HOST, resulting in the URL being https://oursite.com/wp-admin/edit.php?post_type=page&paged=2

Now if we change the WordPress URL back to https://oursite.com, then the admin section works just fine. But the problem here is that I cannot have my admin users considered logged in when browsing https://example.com/subdirectory/

Happy to learn best practices for making this work.