There is an exemption , but you have to research it yourself. My property is not only in a FEMA flood zone ,it is in a FEMA floodway and the site for my new garage was less than 100 ft. from the Connecticut River. I went through everything you're dealing with now. However in my case resolving the issue was quite simple, with no thanks to all those "helpful" Local, State and Federal agencies.
My distrust of government caused me to research the Statutes covering the enforcement of FEMA regulations. When the Town building inspector called to inform me , due to flood zone regulations, he could not issue my requested permit, I informed him of the results of my research.
Giving him the benefit of doubt, he was genuinely surprised, or at least he appeared to be, he stammered for a moment, then said ,he would check with the Town's Legal dept., and get back to me.
The inspector called me the next day ,he apologized for the "misunderstanding" said my permit would be in the mail and gave me verbal authorization to begin construction
FEMA regulations, are just that, regulations they are not duly enacted Laws of the United States and cannot be enforced ex post facto. My home was built prior to 1978, therefore, in my State, Massachusetts, my property is subject to the regulations in effect when I acquired the property in 1972. of course I had to find that out myself. I hope it's just as easy for you.
My garage went up in October, and now with the snow on the ground, my toys have a new home