I remember playing with this model. If you look at the last post in the thread you linked, I modified his sigma4 model to be easier to use. I prefer my own ways of making such models, they are easier for me to grasp.
I am curious about him saying that it is not omni directional? It is when I use it. He did say he wasn't done playing with it yet...
The DB
I made a couple of simple 4NEC2 models that were presented looking like his model details in his post, but I never quite got the hang of using the software performance results. However, I was able to figure out his dimensions. These models were not as complicated as an A/P or a Sigma4. They did not agree with my dimensions, so I asked him, but he never responded.
I think I've seen GHZ24's model of the Sigma 4, and it had a square radial loop. I didn't know how that effected the results, so I asked him about that too. He never responded. I seem to recall later, that I saw his model in Henry's introduction to his report on "The Avanti Sigma 4."
DB, I see a small bit of skewing in my A/P models, but I would not suggest it makes the A/P...not omni directional. I think the skewing is due to the radiator being off-set to one side on the mounting bracket. I have a model where I checked the skewing by locating the radiator in the middle. This made it similar to one of the schematics in the patent. Don't remember the results though.