I'd like to integrate my personal Google Calendar into a 3rd party group scheduling app. The app supports integrating users' personal calendars using iCal URLs; when scheduling an event, it shows an overview of the users' free / busy times so that the best time for the event can be found. When I add my personal Google Calendar using the private iCal URL which can be found in the calendar settings, the app shows all of my events, not just those marked as "busy". Is there a way to modify the iCal feed URL so that the feed only includes "busy" events, and preferably no details other than date & time info, perhaps using query string parameters?
I've tried making my calendar public & selecting the "Show only free/busy info" option and then using the public iCal URL, but apparently that still includes the "free" events, they're just marked as "free", and the 3rd party app doesn't reflect that. Since both the public and the private URLs end in /basic.ics, I'm wondering if perhaps there's a /busy.ics, or a /advanced.ics?filter=... variant. Searching Google for answers to this problem proved problematic because 99% of the search results pertained to importing a 3rd party iCal feed into Google Calendar. None of the variants I tried did the trick (/opaque.ics: 404, /basic.ics?transp=opaque: no effect, ...).