I see the problem you have. The obvious thing to suggest would be to talk to one of the senior planners and see if you can persuade him/her. Give him/her the same info as you've posted here. I have found that planners in general are loathe to admit to a mistake. A bit like referees - they may not always be right but they are never wrong.
Maybe there was a problem in the past with something similar and they are being over-cautious.
Try your local Co. Councillor to see if he can get them to accept what everyone else believes is correct.
You could also try contacting the Dept. Environment for advice.
I have known people to withdraw an application, build and then look for retention but I know you would never consider that
For what its worth I think the garage is exempted development. I have issued certs in the past for garages the same size and indeed slightly bigger but that had to do with property transfer and/or mortgages