At first this was pretty surprising to me, and I was pretty sure it must be a bug in the code. Well, I tried it myself and got the same results. :-)
After a few false starts, here's what I think is the probable explanation. Note that we're trying to approximate √3 by a fraction of the form (ad-bc)/(ac+bd). The closest fractions we get (among a, b, c, d below a given magnitude) could be either below or above √3.
Consider an angle of (π/3+ε). If you look tan(π/3+ε)-tan(π/3), it works out to be (tan(ε) + 3ε) / (1 - ε√3). When ε is replaced by -ε, if you look at tan(π/3)-tan(π/3-ε), it works out to be (tan(ε) + 3ε) / (1 + ε√3).
For small ε, the former, namely (tan(ε) + 3ε) / (1 - ε√3), is larger than the latter, namely (tan(ε) + 3ε) / (1 + ε√3). (More generally, this boils down to the fact that the second derivative of tan(x) is positive.)
This means that it's easier (you're allowed a larger difference in the angle) to achieve a given closeness of the fraction (ad-bc)/(ac+bd) to √3 by picking the angle to be greater than π/3 (=60°) than if the angle is less than π/3.
For larger denominators, √3 becomes about as easy to approximate to a given closeness from below as from above (by fractions of the form (ad-bc)/(ac+bd)), but among roughly equally distant approximations, the ones from above are closer in angle than the ones from below.