I tried to follow your instructions, but my iphone does not list ARCHIVES. I have 50GB storage plan, I have 42GB left, but I too receive the message that I cannot take photos because there is not enough storage.
When I go to SETTINGS > ICLOUD > there is no ARCHIVES listed. I go directly to STORAGE > MANAGE STORAGE > BACKUP OPTIONS. From there I can choose the DATA I want to back up, and most of the data that has backed up is not needed. So I've turned off all those apps that I don't need backed up. But most of them had very little data, like just KB, some 0 KB, so it didn't make a difference.
I still am unable to take photos because of the storage issue..