You need to make some modifications to your cad drawing so it is in line with what the Ackerman Theory is stating. I'm sure once you get things correct in your drawing, you'll find it will work just fine.
I've added some annotations to this image to help you understand where you are going wrong with your example.
First, do you notice that on your example, you have the pivot point (turning point of your tire) right exactly at the edge of the tire. You'll see that in this image, the pivot point (red arrows marked A) is noticeably away from the tire a distance.
Second, the point at which the turning mechanism (red arrows marked B) are a come in board from the pivot points quite a bit. You have this in your drawing, but I'm pretty sure it's not enough. The point of where this point should be at is described as being thus: If you draw a line through the pivot point (A) to the center point of your rear axle (red arrow marked C), the arm pivot point (B) should be located on that line somewhere, but before the rear of the tire (I'm actually guessing on the length of the steering arm, but this length seems logical). It needs to be long enough to provide the difference, but not so long as to tie things up. If I were a betting man, I'd put it at ~70% of the tire radius (NOTE: I did say tire radius, not the swing arm radius). Nevertheless, the point of rotation on the steering arm needs to be located on this line.
So you aren't put out if it doesn't work exactly along the entire turning radius, it won't be. According to Carroll Smith, in Tune to Win he states (pg. 60):
No single intersection point will result in true Ackerman steering over the whole range, but by moving the intersect point in the longitudinal plane, you can come close in the normal range of steering angles.
Once you have these things corrected, I think you'll find your model to work much closer to what you expect.
As a side note, if you want to get technical about it, you could lay it out mathematically. Racetech.com.au spells it out (NOTE: They don't have a clear picture or I'd steal it and post it here. If I have time later, I will remake their diagram and edit this post.)