Your 16-35 is a rectilinear normal lens, so you should mark the images as Normal (rectilinear), and fill in the appropriate focal length and crop factor (1.0) for the 5DMkIII. What I'm not sure of is why you have 72 images.
Full coverage of the sphere with a 16-35 on full frame at 16mm only requires 17 to 29 images. Having nearly three times that many images, unless you're bracketing for exposure fusion or HDR, is probably what's causing Hugin to have issues stitching--the overlap is too large.
If you bracketed for high-dynamic range processing, then you simply need to organize the bracketed sets into stacks. Otherwise, you probably need to remove the redundant images where there's too much coverage of the same area for stitching.
You could use the 8-15L, either at the 8 or 15mm end of the range, and mark the images as either Circular fisheye (8mm) or Full frame fisheye (15mm). The advantages would be that you'd only need eight images: 6 images at 0° rotated in yaw at 60° intervals, a zenith and nadir shot. (If you're really careful with minimal overlap, you might be able to get away with four shots at the 8mm end, rotated in yaw at 90° intervals), but your resolution, and probably your image quality, will be lower than if you use a rectilinear ultrawide.
I've successfully used the Sigma 8mm f/3.5 fisheye on my XT, 50D, and 5DMkII, as well as the Rokinon/Samyang 7.5mm f/3.5 for micro four-thirds on my GX7. The Sigma 8mm f/3.5 for dSLRs is a popular low-cost option as a pano shooting fisheye lens, but if you already have the 8-15L, you don't need it.