You ARE covered by FOPA, and if arrested while actually following FOPA you will not be convicted. However, if you make one slip, you will be prosecuted to the full extent of the law.
If you are driving, drive straight through (course of normal travel). If you are flying, you could get into trouble. For example, if you are making a connection and get laid over in DC, and they give you your luggage (with gun case inside) back(!!!), you are then in illegal posession of a firearm. Case law will eventually make this legal, but for now, at least two courts have upheld convictions.
Best advice is of course to avoid any city that will arrest you if possible. There is no reason to go through DC, as it is faster to go around. If you HAVE to go through DC, you must be doing business there. In that case, you are obligated to follow their laws. So, before you get there, mail your firearm to yourself at a legal destination.