Verification Required Loop

Attempting to install or update any apps results in a popup that says "Verification Required. Tap Continue and sign in to view billing information."

Doing so simply repeats the process, and all help I have found has resulted in no change.

I have changed my apple password twice, re-entered my billing information twice, restarted my phone three times, and tried continuing by selecting "None" for payment options four times.

If anyone else has had this same issue and resolved it without selecting the "None" payment option like all other posts I've seen suggest, please let me know. I would like to update my apps and continue using the app store.

Thanks.