Game Center id interfering with iCloud login

Using High Sierra on an iMac on my work computer.

I am trying to log back into my iCloud account on an old iMac computer that I have been using for years. Was getting iCloud messages about some services not available until I log back in, so I completely logged out of the iCloud account on that computer.

So, to re-log back into the iCloud account on work computer:

I go to System Preferences>>Internet Accounts>> add iCloud

enter the correct email address and password firstnamelastname@me.com

this creates a Game Center account with the user firstnamelastname@me.com

I try to activate the iCloud account

the user shows up as just firstname lastname instead of the firstnamelastname@me.com

I try to enter the password, but it is rejected. I know the password is correct because the password works with my iPhone and iCloud account in Safari.

I have: tried this repeatedly, changed the password, done restarts of the machine, run Disc Utilities.

It seems to me the Game Center id is causing the problems. Tried deleting that a number of times.

I am unable to check my email via AppleMail, nor see my iCloud iCals or Address Book entries on this work computer. But I can see the associated GMail accounts.

Really like using AppleMail at work as I monitor 2 work gmail accounts, 1 personal gmail account in addition to my personal iCloud account.