Can't add gmail back to iphone

I had 2 Gmail accounts on my iPhone 6S, and I changed the password on one of them on my PC.

Then I had to enter the new password on the phone; no matter how many times I entered it, and got a verification code, and responded to the email (on my PC) that the activity was me, it would NOT accept it on the phone & let me back into my account.

I removed the account from the phone, and tried to add it back - same loop occurs and will not add the account back. This account has ALL my contacts, which of course is causing problems. I have read forums and tried everything - I don't know how to make this work.

Here's the loop:

• settings, mail, accounts, add account, Google
• sign in screen: enter email - NEXT - enter password
• 2 step verification - enter code
• go to Gmail email on my PC - respond to security alert and confirm it's me
• nothing in the list for the new account
• tried shutting phone down - nothing

Any suggestions??