The "distortion" is caused by a too close working distance, resulting in an objectionable difference in magnification of the near and far points of the sitter. It is exactly the same problem as filling a 35mm frame with a face... with a 20mm lens.
Move the lens away from the sitter, the magnification difference diminishes, and the problem is solved. And, when the image size is equalized by enlargement of 7.2 times, the 50mm lens makes exactly the same image as the 360, from the same distance from the subject.
Like the 50mm on a 35mm camera, 2 meters is reliably safe for a 360 on 8x10, 1.5M is usually OK, and 1.2M is acceptable if you are careful about where the ears and nose are aimed !
And like 35mm, where the small difference between a 50 and a 60 for close up work makes all the difference in a portrait, going from a 360 to 480 makes all the difference in a tight composition.
Practically, though, it is FAR EASIER to compose a portrait loosely on 8x10,
and enlarge the 6x8 / 15x20cm portion of the film, for which 360 is perfect ! Or, compose a head and shoulders image in the 15x20cm core of 8x10 film, and use the remainder of the filed for 'context'.
My 360 Imagon, in Compound, covers 8x10 sufficiently from 2 meters to never have a worry. I think for critical use ( this is silly ) you shouldn't expect it to image more than a 250 mm circle at infinity. Thankfully, the edge of the image circle is not abrupt and we can really get away with a lot with the lens.