@lore My EFI partition only has 1 file: EFI/APPLE/EXTENSIONS/Firmware.scap
My installation has a separate "Boot OS X" partition. I'm using Apple mirrored RAID (the one that predated CoreStorage) so my partition layout might be very different from what you are looking for.
I have a 10.9 recovery flash drive somewhere, I'll see if I can find it. Are you sure 10.9 is what you want, I was pretty sure you've been using something more recent 🤔