Ditto guys, I'm stuck on the same damn staircase.
I'm using sixtyforce emulator and a retrolink USB controller and I think this controller's sensitivity might be a little shoddy. (bad workman always blames the tools)
The biggest problem for me is that Link jumps whenever he gets too close to a ledge. If you know about the infinite sword glitch (google it if not) and can find a way to trigger it in this room then it might help, one side effect of ISG is that Link cannot fall off of ledges while this is active. However, I'm not sure there's a way to engage ISG in this room. If anyone's found a way let me know.
Until then, keep trying I guess... "Be the path!"