A hidden exchange account

Yesterday my Nexus 7 (first gen) upgraded OTA from Android 4.x to 5.0.2 (Lollipop).

After the upgrade completed I opened the Gmail app and it now shows both my normal Google account and my business email account (Microsoft Hosted Exchange).

Yet for my Exchange account I only see the folders in the Gmail app, no messages and no calendar entries. When I try to delete the account it is simply 'not there' in the list of accounts (under settings -> Personal -> Accounts). Trying to add the account with the same email address gives the error "Duplicate account".

Perhaps relevant: The company I work for has some policy settings requiring a PIN on the lock screen.

I did find this thread but I'm not willing to root my device just to remove an account. http://ift.tt/1IKp8ya

For me simply being able to delete this Exchange account and creating a new one is good enough for me.

How do I do that?