There are a *LOT* of folks here who know a lot more than I do .... and they'll be fast to blast me if I'm wrong.
First, welcome to the joys of commercial vs recreation. Commercial has to have authorization, where recreation only has to notify. It doesn't seem fair, does it?
Looking at the airspace, LAANC is not active for Burlington, so that's not an option. There are a lot of Zero grids directly around the airport, as expected, and then expanding out to 100, 200, and 400 feet available to be authorized.
So it seems at this point, you can not get the authorization you need from the airport. That leaves you with going through the FAA and requesting it. You can request a waiver, using the facility map grids as references for your maximum altitude. The process takes time, but once completed, it would give you the ability to fly, at least outside of the zero grids.
For actual flight over the tarmac for next year's fly-in ... that's a little tougher. That will require extra authorization and release of the NFZ by DJI, or use of a drone that doesn't have the NFZ restrictions.