I tried a flat basket on slab of boneless salmon fillet, and I was not happy at the results. The heavy chrome center bar squish-cooked a heavy dent down the centerline of the meat .
It even overcooked that area because the increased heat transfer of the heavier bar.
This hard impression made the salmon look sooo UGLY!
I cannot imagine a whole fish with its thickest point under that center bar would fare much better, IMHO.
I think the better idea is shown in the photo above, using only fish steaks...or perhaps dispensing with the basket altogther for fillets and larger fish steaks, and using the hot/clean/oiled grill method Steve R. speaks of so often. This also is considering the extra time needed to clean the rotisserie basket after all is said and done.
If I can ever get some photos posted, I will post a pic of this turner I got from my pops that is OLD...carbon steel, 3" wide, 1 foot long (not including handle) and is beautifully THIN and rather flexible. It works great for flipping things like fillets, fish steaks, and two burgers at a time!