Matt,
thanks for creating the document, it was a lot of fun doing this! It's actually quite a challenging cognitive task, going through more than 250 (that's what I calculated, correct me if I'm wrong) comparisons in a row in your mind. That requires some concentration if you want to treat every comparison with equal attention.
My own rankings are pretty similar to what I would've otherwise ranked them, with a few exceptions that I might have an explanation for. One aspect that I noted might benefit from this method is remoteness and scenery of courses - for example, I would split rounds between Carne and TOC 5:5, since TOC has the architectural interest and history, but Carne has the feeling of remoteness, the spectacular beauty and is less crowded. This effect vanishes when comparing two similarly remote courses, in my case Carne and Machrihanish, which I would split 4:6, since Machrihanish has a similar feeling of remoteness but is architecturally more interesting. Yet, I would have normally ranked TOC above both Machrihanish and Carne.
Another thing that might distort the ranking is having courses that are very different from the rest of your list. For example, Kingston Heath was pretty much the only proper inland course that made my list, and however good a comparing links course was, I was pretty biased towards a 5:5 ranking, since splitting it this way between almost any interesting seaside links and Kingston Heath is a pretty nice prospect for sheer variety. Even though I would have normally ranked Kingston Heath above many or most of these links. But this effect, if it is one, might work the other way around aswell.
In other words, what I would argue is different ranking courses this way compared to any other way is a) the experence over mere quality of the courses and b) courses that stand out from the rest in some way.
In any case, what a fun excercise, thanks.
Emil