Thank you all for your replies. I was going to multi-quote, but everybody had something useful to add. I am not experienced with fisheye lenses so everything was helpful.
A little more info, as brief as possible.
First, a mistake. The lens I purchased was not a Rokinon but this Opteka. For the price I paid ($150) I am very happy (shocked) with the image quality.
I shoot primarily with three cameras: 5D2, T3i, and 5D. The Opteka on the T3i creates superb full frame images - great wide angle distortion style edge-to-all-edges. But on the 5D it creates the full sphere images, surrounded with black. Cropping these down to full frame edge-to-edge nets a very small image.
My desire is to get the same edge-to-edge wide angle, 180 degree distorted look on the 5D.
As to why, it is because the 5D is an IR conversion and I want the style when shooting IR.
So I only have two choices:
a) Buy another crop camera such as another T3i and have it converted, or
b) Buy a fisheye that can be used on the FF 5D.
I figure both will cost about the same, but (b) buying the new lens will have the added bonus of also being used on the 5D2. It would also mean I can put the Opteka on the T3i and the new lens on the 5D and shoot without lens changes.
Hope that makes sense. It is very important to me to get the distorted wide angle fisheye effect when shooting IR, but again I do not have a crop sensor IR conversion so cannot presently do so without unacceptable cropping.
Again, thanks for the info.