Aren't odds ratios multiplicative? It also seems to me that we should take the center of the SAT score bins to avoid an off-by-one bin width bias, so (10.381 / 1.907) ^ (10 / (1550 - 1350)) = 1.088. (Or compute additively with log-odds.)

Yeah; Vaniver already did it via log odds.

If we look only at the top two SAT bins in Model 7: (10.381 / 4.062) ^ (10 / (1550 - 1450)) = 1.098.

Which is higher than the top bin of 1.088 so I guess that makes using the top bin an underestimate (fine by me).

Note that within the logistic model, they binned their SAT score data and regressed on them as dichotomous indicator variables, instead of using the raw scores and doing polynomial/nonparametric regression

Alas! I just went with the first paper on Harvard I found in Google which did a logistic regression involving SAT scores (well, second: the first one confounded scores with being legacies and minorities and so wasn't useful). There may be a more useful paper out there.