I'd just wait it out.
For -months- I couldn't log in or out of iCloud on my Mac after I changed my contact email for my Apple ID via my iPhone. iPhone was fine. Mac was hosed.
Then suddenly 2 months later it logged in with no issue. I didn't change or do anything different. It just suddenly worked.
In my experience, iCloud syncing on all your devices is a miracle that rarely occurs without hiccups.