page_link is not going to work as even though you change what it shows or uses, that’s not going to be detected when the URL is accessed — which requires handling to parse it during the request.
You could look at adding rewrites, or what is probably easier you could use try using something like this (or view their code to see how they do it):
https://wordpress.org/plugins/custom-permalinks/
Here’s how they are doing it:
https://plugins.trac.wordpress.org/browser/custom-permalinks/trunk/frontend/class-custom-permalinks-frontend.php