This problem appears to finally be solved with the new "RingCentral for Windows"!!!
This now fully restores integration with MS Office, even Office 365. I'm running version 126.96.36.19919. It sees Outlook, installed the Add-In, syncs with contacts, etc.
It's a whole new interface, with some annoying rough edges still, like RingOut requiring a combination of key presses and mouse clicks to initiate a call, and the fax system no longer allows editing or stamping signatures in faxes before sending. But I assume these will get better in future updates. Overall, for me, with Office 365/2013 compatibility, it's already much better than the old "SoftPhone" application.