he never addresses things like the supposed is-ought problem properly. He just handwaves it by saying it does not matter, as you point out, but this is not what I would call addressing it properly.

I don't know. What more is there to say about it? It's a special case of the fact that for any sets of sentences P and Q, P cannot be derived from Q if P contains non-logical predicates that are absent from Q and we have no definition of those predicates in terms of Q-sentences. All non-logical words work in the same way, in that respect.

The interesting question isn't Hume's is/ought distinction, since it's just one of a billion other distinctions of the same sort, e.g., the penguin/economics distinction, and the electron/bacon distinction. Rather, the interesting question is Moore's Open Question argument, which is an entirely distinct point and can be adequately answered by: 'Insofar as this claim about the semantics of 'morality' is right, it seems likely that an error theory of morality is correct; and insofar as it is usefully true to construct normative language that is reducible to descriptions, we will end up with a language that does not yield an Open Question in explaining why that is what's 'moral' rather than something else.

I agree Harris should say that somewhere clearly. But this is all almost certainly true given his views; he just apparently isn't interested in hashing it out. TML is a book on the rhetoric and pragmatics of science (and other human collaborations), not on metaphysics or epistemology.

The reason his answer is not obvious is that it assumes that what is desirable for the aliens must necessarily be desirable for us.

Ideally desirable, not actually desired.

In other words, it assumes a universal morality rather than a merely "objective" one (he assumes a universally compelling moral argument, to put it in less wrong terms).

No. See his response to the Problem of Persuasion; he doesn't care whether the One True Morality would persuade everyone to be perfectly moral; he assumes it won't. His claim about aliens is an assertion about his equivalent of our coherently extrapolated moral volition; it's not a claim about what arguments we would currently find compelling.