I have an idea for a very simple quadra test. The test would tell you what quadra you are and nothing beyond this.
The idea is to simply display the images of people that have been typed reasonably accurately at random and to ask the observer to rate their level of subjective attraction to the person in the image. High attraction ratings would increase a value representing the likelihood of the person being in the same quadra as the person in the image. Low attraction ratings would decrease said value.
The reason why such a test would be useful is because it circumvents a lot of the problems with the unreliability of self-report. The test would largely operate of subconscious evaluations (attraction) and thus defy the thought process by which a person tries to "convince themselves" they are one type or another.
A good place to start would be to take Rick's typings and images in the celebrity section of his website.
Do people here generally feel that typing by means of visual assesments of attraction works? Subjectively, I think it does in my case. I find it hard to even look at a picture with a conflictor of mine in it.