Apple Verification Code dilemma

Apparently I cannot recall my Apple ID password (on my iPhone), so... I select "forgot code," enter my Apple ID, then enter my Apple Recovery Key, and I wait for my code to arrive as a text. However, once I go to my iMessage screen to retrieve the code I cannot return to the code entry screen (without initiating the cycle all over again (when, of course, I'll be prompted to add a different code).

Where am I completely missing the boat?