Creating surface from .adf file - Scale of Coordinate system is off

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I'm having an issue with scaling that concerns my coordinate system while creating a surface from a .adf file (NED Data). The file is a 1x1 degree tile with elevations in meters. I had to convert the file from meters to feet which I did by exporting the XML and then loading it into an imperial file successfully with each file set to the correct coordinate system. My issue is the scaling of the file itself. The 1x1 degree grid comes in as 1'x1', and the coordinates are correct within that tile. The issue is this 1x1 degree tile is not 1 square foot and I need the scale to be in a real world setting to lay out other features on the surface to scale. Does anyone have any experience with this or have a suggestion on how to adjust the CS or file to make the distances accurate? In the real world the distance between latitudes is something like 360,000 feet, not 1.
I have already tried scaling the surface but this obviously then makes a huge discrepancy with the coordinates within the file, since they align with the 1'x1' tile. Any help is greatly appreciated since I can not move forward with my design without the correct distances between the lat/longs.
Thanks.