My very vague and silly guess is that among women in my age range, she was more compatible than about 49/50 of the others. And what I'm looking for is more like 1/300 or 1/400.

Thank you for clarifying what you mean by extreme compatability. I did not misinterpret what you meant.

Consider all the women between 22 and 60 in the eastern part of Marin County, California. Note the extremely broad defintion of "my age range." (Again I'm 49) Not all the single women, but all the women, single and looking, single and not looking or married. My next girlfriend will come from this set with probability .9 or more unless I move, which is very unlikely. (Of course she is more likely to come from the subset of those not now married.)

Now (using Pearl's language for causal models) do surgery on my model of reality so that I am already in a sexual relationship with one of these women picked at random. Do additional surgery so that she and I already know each other at least as well as couples usually do. Acquiring this knowledge is very time consuming and entails costs like dinners and entrance fees to cultural events. Note that this second bit of surgery allows me to consider the merits of the woman picked at random without regard to whether those cost (again, mostly my time and attention but also entrance fees, etc) are better spent on a different woman.

Marin County is among the top 3 most affluent counties in California. Demographics similar to Silicon Valley, but replace the nerdy component with earthy-crunchy and new-age components. Probably .1 (10%) of these women work out with weights regularly and a significant fraction employ personal trainers to help them keep in shape. (An ordinary trip to the supermarket is often a very distracting and very vivid experience for me )

There is a higher than .5 probability that I would choose to stay in the relationship until she dumped me or 36 months have gone by. The only reason the 36 months is in there is so that I do not have to consider the effects on my attractiveness to women (and consequently, my dating options) of a significant change in my circumstances.

The most likely reason I would choose to dump the woman is that her thinking is significantly distorted by some ideology, and I consider progressive political beliefs an ideology -- in fact, it is IMHO the most common ideology in these parts.
Or maybe what I am reacting to is just a high amount of the Big Five personality trait agreeableness. (I am quite low in agreeableness.) Speaking of Big Five, I am an extreme introvert, so strong extraversion is probably something else that would drastically lower the probability that I would choose to try to keep the relationship going as long as possible (inside this 36-month interval that defines our current universe of discourse). I could go on and on, but you get the idea.

Would I prefer that she has read all of Eliezer's writing on the art of human rationality? Of course.

But I would be delighted, overjoyed, elated if she just knew the correct definition of "sexual selection" or understood that the poor people in the England of Charles Dickens were in fact materially better off than almost any other poor population at that time or at any previous time in history. (Define "poor population" as the first seven deciles of individuals distributed by material welfare in some natural category of people, e.g., residents of a nation state or linguistic community.) In other words, delighted, etc, if she had enough rationality, basic knowledge of things like the timing of the Industrial Revolution, and curiosity to seek out the hard numerical data which contradicts and overrides the fictional evidence of dramatizations on PBS of Charles Dickens novels. I just ended a 5-year relationship with a woman who did not know these 2 things. (She dumped me.)