Invites go into the wrong Calendar - and can't be changed

I've seen many other people have this problem, but none of the ways that solved it for them, did it for me.

When I get invites, they always go into my private calendar (gmail). While 99% of them should go into my work calendar (iCloud).

I've tried

- putting the iCloud calendar on top in iCal

- changing the default calendar to my work calendar in Preferences

- putting my iCloud calendar on top in the Settings > Internet Accounts

- changing it manually (it won't show me other calendars as an option)

Short of calling Apple Support, I think I've tried everything?