As far as I know, checking vit https will only check if IIS is running. As you stated the content returned by IIS is static and then from there it's based on API calls done by the browser.
You could maybe add an aspx page, something like check.aspx, and do from there a simple API call, for example, try to authenticate as a user used for the check and return SUCCESS / FAILURE depending the result of the call.
Then use your monitor tool pattern matching.
It's a bit unconvenient but I have no other idea ...
Sébastien Riccio
System & Network Admin
https://swisscenter.com