If one defines morality in a utilitarian way, in which a moral person is one who tries for the greatest possible utility of everyone in the world, that sidesteps McCarthy's complaint. In that case, the apex of moral progress is also, by definition, the world in which people are happiest on average.

It's easy to view moral progress up to this point as progress towards that ideal. Ending slavery increases ex-slaves' utility, hopefully less than it hurts ex-slaveowners. Ending cat-burning increases cats' utility, hopefully less than it hurts that of cat-burning fans.

I guess you could argue this has a hidden bias - that 19th century-ers claimed that keeping slavery was helping slaveowners more than it was hurting slaves, and that we really are in a random walk that we're justifying by fudging terms in the utility function in order to look good. But you could equally well argue that real moral progress means computing the utilities more accurately.

Since utility is by definition a Good Thing, it's less vulnerable to the Open Question argument than some other things, though I wouldn't know how to put that formally.