File order on FAT/FAT32/VFAT file systems

I have several audio devices (car radio, portable radio, MP3 player) that take SD cards and USB sticks with a FAT file system on it. Because these devices have limited intelligence they do not sort filenames on the FAT FS by name but merely play them in the order in which they have been copied to the SD card. In MS DOS and MS Windows this was not a problem; using a simple utility that sorted files alphabetically and then copied them across in that order did the trick. However, on Linux the files copied from the ext4 file system do not end up on the FAT FS in the same order as in which they were read and copied across, presumably because there is a buffering mechanism in the way which improves efficiency but does not worry too much about the physical order in which the files end up on the target device. I have also tried to use Windows in a Virtual Box VM but still the files end up being written in a different order than the one they were read from the Linux file system. Is there a way (short of copying them across manually one by one and waiting for all write buffers to be flushed) to ensure that files end up on the FAT SD target in the order in which they were read from the ext4 file system?