The Files on the SD Card are all on the root directory of the SD.
Well, this is the main problem. Even when you get relative paths working correctly, and it does work correctly, MC is going to export the playlist with full paths to the sub-directory locations it knows about in the MC Library.
So if your music files are in say "M:\Music\Pet Shop Boys\Actually\", and you have the SD card mounted as F:\, and you use relative paths, and you save the Playlists in F:\Playlists, then the path in the Playlists will be;
.\..\Music\Pet Shop Boys\Actually\
That is, the path to the files is relative to the location of the Playlist.
There is no way within MC to strip the path down to just F:\, so that a file called "M:\Music\Pet Shop Boys\Actually\Pet Shop Boys - 01 - Actually - One More Chance.flac" is found in "F:\Pet Shop Boys - Actually - 01 - One More Chance.flac".
But you can edit the Playlist file to make that happen.
But why did you put all the files into the root directory? Generally, that is a very bad thing to do. There are restrictions on the number of files that can be stored in the root directory of any device, usually imposed by the OS in use, but also by the device format.
In your situation, unless the DAP requires that files be in the root directory, I would use the
Sync Handheld functionality of MC, sync to the SD card on the PC, and use relative paths. Even if you don't use the same sub-directory structure as used on your NAS, MC will write the correct paths to the files, based on your settings in Sync Handheld. Then all should work.