Let me phrase it differently: What do you want to achieve with passing the emailid as a query parameter? 

Reverse replication was never supported in AEM CS: https://experienceleague.adobe.com/en/docs/experience-manager-cloud-service/content/release-notes/aem-cloud-changes#replication-agents

Sorry, my bad. Forgot that the latest AEM 6.5 SP updated Oak to a very recent version as well, and was a bit confused  Seems like https://experienceleaguecommunities.adobe.com/t5/adobe-experience-manager/installing-aem-6-5-with-s3-connector-and-install-service-pack-4/m-p/364219 is pretty much the sa...

May I ask what version of AEM you are using? It's not AEM 6.5 and it's not AEM CS...

Why is the OOTB SAML authentication not enough? What do you want to achieve?

How do you deploy this file? Via fullstack pipeline or frontend pipeline?In case of the fullstack pipeline: Not a problem, as new instances will be started with an empty dispatcher cache. So you don't need to invalidate them.Frontend pipeline: Good question, I am not an expert in that ... would need...

Can you please point me to the documentation which says that SAML 2.0 authentication on publish is not available on AEM CS?(I know a number of cases, where this is working.)

Where did you configure the statfilelevel? It's only respected in the farm which is used by the invalidation requests.

when you replicate that page (and therefor trigger an invalidation), at which directory is the closest .stat file?

can you post a minimal HTL scriptlet with hardcoded values, which demonstrates this behavior?