You have to spend a pretty ridiculous amount of time to get 4 FEOKs. I did it in Sylx Tower. It's not quite so bad with frame skip and save states I guess. I can't recall if you can run into any of the dragons up there. There is a pattern to encountering them in the Sylx Tower. I wrote a guide to it a while back but it's somewhat out of reach atm... I may look it up later.

However, if you have no saves outside of the Dark World you may be out of luck.