James
I only hit worm-burners by mistake!
As to the question, I can think of a lot of "island" greens on 4s and 5s as well as a few "biarritzis" and "redans." Don't think that "edens" would work and I really don't know what a "short" is except, well, short. If that's the case, most par-4s have "short" greens since the guys are hitting wedge into them these days!
I think the redan concept works great, but architects don't seem keen on designing too many front to back sloping greens, probably becuase the punters don't like them.