Make a disk image formatted with both ext2 and FAT, at once.
~/cursedfs% wget 'https://github.com/NieDzejkob/cursedfs/releases/download/v1.0/cursed.img' ~/cursedfs% sudo mount -o loop -t ext2 cursed.img mountpoint/ ~/cursedfs% ls mountpoint/ mkfs.cursed ~/cursedfs% sudo umount mountpoint/ ~/cursedfs% sudo mount -o loop -t msdos cursed.img mountpoint/ ~/cursedfs% ls mountpoint/ gudnuse.ogg
It turns out this is surprisingly simple to do: just create a FAT volume with a lot of reserved sectors and put the ext2 into the reserved sectors. This works because the filesystems choose different places to put their superblock: FAT uses the very first sector, while ext2 leaves the first kilobyte unused.
Can I write to the filesystems?
Yes! When I first decided to do this, I thought writing to the image would surely break everything, but as it turns out, the method I've found means the filesystems don't conflict.