So it will not be technically a garage when it is enclosed just with screens.
You will need a new plat drawing for all improvements in your house, as long as they have an impact in the foot print, or if the repairs or alteration change the function of any of the areas described in the drawing. In your case, since you’re changing the “nature” of the carport to that of a garage, you will need it.
A plat is different from a survey. What you are mentioning is an opine representation of what was in your lot, and what you need to do is to order a new survey of the property. For that you need to hire a certified surveyor in Washington DC (The office of the Surveyor of Washington DC, located at DCRA has a list of the surveyors that work in the city, and are certified in the district of Columbia, please notice that this service is a private contract between you and the surveyor, the city doesn’t recommend or endorse any of them, nor they regulate the fees they charge. This is the list of the surveyors: http://dcra.dc.gov/node/509332)
They cannot count against you any structure that no longer exists in the parcel.
To ask for the permission to enclose that part of the structure and transform it into a garage you need a set of permit plans, which will refer to the new survey and new plat (your surveyor will do the survey, and any additional information about the improvements of the house will appear in your permit set, and also in the plat -part of the permit set-that is required to demonstrate that there are or there aren’t changes in the footprint)
If you need more information you can e-mail me at odcstudio AT aol DOT com.