Had the exact same issue. Not sure what you meant by "played with the icloud settings", but this worked for me:
Go to Settings > iCloud, and move the toggle switch from OFF to ON
Exit the Settings and go back to the Calendar app. If you're lucky, you will now see both the Calendars button and the + button, or at least that's what finally worked for me.
Optionally (assuming this worked for you), you can now go back into Settings and disable iCloud syncing of your Calendars. It will prompt you to either Keep on My iPhone or Delete from My iPhone (I chose Keep), and your + button should still be there. Hope this helps.