(1) My first thought was that this (at most) merely shows that moral reflection is inert at the margin. Other academics ("non-ethicists of similar social background") are still reflective people, and so presumably give a reasonable amount of thought to moral issues. So this common core of reflection might be very effective, compared to someone who engaged in no moral reflection whatsoever. But if moral reflection yields steeply diminishing returns, this could explain why the extra reflection of ethicists doesn't seem to have any additional effect.
(2) Roman Altshuler proposes a 'Hume-Strawson model':
Perhaps moral deliberation makes no difference to our behavior directly. But maybe it does make a difference to how we judge others. If moral reflection does structure our reactive attitudes, and the reactive attitudes of others does have some effect on our behavior, then moral deliberation is not entirely inert. It is simply that its effects on behavior occur through very indirect mechanisms.
(3) Brandon suggests something like the 'virtue theory' picture, whereby ethics is a distinctively practical skill rather than simply a matter of rational theorizing. (Cf. "the relation between physics and sports.") This would again make the effect of moral reflection very indirect. Having worked out what sort of person one ought to be, it's quite another matter to actually inculcate the right dispositions and habits, etc.
(4) Schwitzgebel's own suggestion is the 'bivalent view' that moral reflection affects our behaviour, in particular reducing conformity to prevailing social norms, but this is not always for the better (due to rationalization).
(5) Selection effects: maybe ethicists were disproportionately bad people to begin with!
Any other suggestions? Which (combination) of these do you give credence to?