Endless "Verification Code" loop while creating new Apple ID; code is verified, then resets and asks again
Newly purchased refurbished iPhone. (Factory unlocked, works perfect.) Just installed the latest iOS (10.3.3). Want to create an Apple ID. Successfully follow the steps to set up an ID with no payment method -- i.e. go to App store, choose random free app, click "Get," then when it asks me to log in click "Create new Apple ID," then correctly fill out all the required fields, choose "None" as payment, the fill in the rest of the fields correctly, then get to the final page which says "Email verification," check my email (on a separate computer), get the code, enter the code correctly into the "Verification code" field, click "Verify," the circle spins for a few seconds and the code is accepted and verified, and a blue check mark appears next to "Verification code," indicating that everything was done correctly, the code was accepted, and the account verified.
You may be wondering, "Well, what's the problem, then?"
Here's problem: After the blue check mark appears indicating that the code was accepted and the account verified, nothing happens at first -- I just stay on that screen and it doesn't take me automatically to the "Yay! You've created a new account!" screen. And THEN, even worse, after several seconds, the verification field goes blank again and once again says "Verification Code: Required" where I had just typed in the correct code moments earlier, and the "Verify" button reappears -- as if I hadn't just done it.
So I type in the correct verification code again, it gets accepted again, for a few seconds I seem to have an account again, and again stare at the screen waiting for it to complete the process -- and again the verification goes "poof" and undoes itself.
There seems to be no way to escape this loop other than to go "back" to the previous page where I filled out my address, but from there I can only once again return to the Verification page where once again I do everything right and the process repeats as above.
I've searched the support archives here and could not find anyone having this exact problem. Everyone else seems to have problems getting the email with the code (I get the email fine), or are wrestling with an existing account.
I tried resetting the Network settings, turning wifi on and off several times, restarting the phone -- all to no avail. Oh, and of course each time I restart I try to enter the account email and password (hoping that the verification DID stick) but I inevitably discover that the account has NOT been successfully created, and I have to start all over again. And get back into the same endless loop. I am definitely connected (via wifi).
Help! How can I create an Apple ID for my new phone and get out of this frustrating cycle?