My view on operations in controlled airspace is that all that is required is permission from the ATC controlling facility which in the case of D, C, and B would be the tower. Class E controlling agencies can be a little trickier to find.
Operations in C and B are more than likely out considering you have to have a Mode C transponder for operations in their airspace. If I were to try an operation in D surface area, I would call the tower on the phone a few days prior and have exact coordinates, distance from airport, altitudes and times of the operation. I would have a VHF radio to be able to communicate with the tower during the operation. This might be overkill but the more professional and organized you are, the more likely they are going to allow you to operate in their airspace.
One quick note on Class E. There are not a ton of areas in the country where you would be operating in class E if you are adhering to the 400 AGL limit. They floor of the vast majority of class E is 1200 AGL. Around some airports there is a transition area where the floor drops to 700 AGL. There are some areas that class E extends all the way to the surface, but you do not see that very often, especially in the eastern United States. So if you are below 400 AGL, you are below the vast majority of class E in the United States. This is why it is so important to understand your sectionals.