Does the proper expiry time show from the accounts page? i.e. https://secure.eveonline.com/AccountManMenu.aspx
At least one problem is that CCP has retired the XML API function that would normally provide this information (http://eveonline-third-party-documentation.readthedocs.io/en/latest/xmlapi/account/account_accountstatus.html) but of course that API is also inaccurate as you noted above. Moreover, the ESI doesn’t (yet) contain an equivalent function.
If the accounts page shows the proper information, then it should be possible to script an SSO app which can pull this info off the page. I don’t have a PLEX’d account so I don’t know if the info is accurate.