So Evolution, available in the Software Boutique, also has complete Google integration. Thunderbird in Ubuntu MATE 15.10 and 16.04 onwards also comes pre-installed with the required extensions to integrate with Google Contacts and Calendars.
Both have worked for me, I’ve not seen the issue you’re running into 
For Google Drive integration I recommend InSync, also in the Software Boutique. It is proprietary, but so is Drive, and costs $15 but offers a Dropbox like symc solution.