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LFGSS #buyer solution: buy a high-end server and pay a lot of money to keep it in a datacentre so you can run a tiny script and make your calendar-life a little easier.
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Doesn't look like Google supports auth so an export->public might be your only solution:
https://productforums.google.com/forum/#!topic/calendar/vjSZRkJHaWA -
Library looks like it does a lot of calendar-related shit, will need server
http://sabre.io/vobject/
http://sabre.io/dav/ics-export-plugin/
What can you export the calendar as? Do you have a server you can run a regular export script on, make it public via http or something and then get your googs to pick that up?