The city could be correct about the lack of permits or not. I would never take it with out trying to push all the buttons I could starting with backing them off the 10 days to remedy issue. If you take the tiger by the tail method, do everything in email, if they to respond with emails follow up with emails anyway. Write emails about everything you discuss to as many people as you can.
These people are not above a shakedown,not above withholding a more simple remedy from you, that they know about and that others have won.