Copying my earlier reply from a 1:1 conversation in this thread with Saumin:
It would probably be best to run pagespeed post url-rewrite.
(The module makes a lot of efforts to be the first module to see the pristine / unmodified url, but it is possible that another module
beats it to that and changes it if module ordering is an issue. It's never come up as an issue before though).
Having said that, the url that should be purged is the url that pagespeed "observes" as it comes in on the webserver.
It's not possible for me to figure out what that looks like from here, and looking at the output of the server will not help
either.
Capturing a trace with DebugView may also be helpful, to see what the world looks like from pagespeed's perspective:
https://www.iiswebspeed.com/documentation/diagnosticsOtto