I certainly wouldn't, and here's why.

Mentioning "non-human animals" in the same sentence and context along with humans and AIs, and "other intelligences" (implying that non-human animals may be usefully referred to as "intelligences", i.e. that they are similar to humans along the relevant dimensions here, such as intelligence, reasoning capability, etc.) reads like an attempt to smuggle in a claim by means of that implication. Now, I don't impute ignoble intent to the writers of that declaration; they may well consider the question settled, and so do not consider themselves to be making any unsupported claims. But there's clearly a claim hidden in that statement, and I'd like to see it made quite explicit, at least, even if you think it's not worth arguing for.

That is, of course, apart from my belief that animals do not have intrinsic moral value. (To be truthful, I often find myself more annoyed with bad arguments than wrong beliefs or bad deeds.)

Those who have thought most about this issue, namely professional moral philosophers, almost universally agree [...] that it's wrong for people to consume meat and perhaps other animal products

Citation needed. :)

As an anecdote, Jeff McMahan mentioned at a recent conference that the moral case for vegetarianism was one of the easiest cases to make in all philosophy (a discipline where peer disagreement is pervasive).

It's interesting that you use Jeff McMahan as an example. In his essay The Meat Eaters, McMahan makes some excellent arguments; his replies to the "playing God" and "against Nature" objections, for instance, are excellent examples of clear reasoning and argument, as is his commentary on the sacredness of species. (As an aside, when McMahan started talking about the hypothetical modification or extinction of carnivorous species, I immediately thought of Stanislaw Lem's Return From the Stars, where the human civilization of a century hence has chemically modified all carnivores, including humans, to be nonviolent, evidently having found some way to solve the ecological issues.)

But one thing he doesn't do is make any argument for why we should care about the suffering of animals. The moral case, as such, goes entirely unmade; McMahan only alludes to its obviousness once or twice. If he thinks it's an easy case to make — perhaps he should go ahead and make it! (Maybe he does elsewhere? If so, a quick googling does not turn it up. Links, as always, would be appreciated.) He just takes "animal suffering is bad" as an axiom. Well, fair enough, but if I don't share that axiom, you wouldn't expect me to be convinced by his arguments, yes?

I mention this, not as evidence that the issue is completely settled, but as a reply to your speculation that there is even more disagreement in the relevant community outside Less Wrong.

I don't think the relevant community outside Less Wrong is professional moral philosophers. I meant something more like... "intellectuals/educated people/technophiles/etc. in general", and then even more broadly than that, "people in general". However, this is a peripheral issue, so I'm ok with dropping it.

Frankly, I'm baffled by your insistence that the relevant arguments must be found in the Less Wrong archives. There's plenty of good material out there which I'm happy to recommend if you are interested in reading what others who have thought about these issues much more than either of us have written on the subject.

In case it wasn't clear (sorry!), yes, I am interested in reading good material elsewhere (preferably in the form of blog posts or articles rather than entire books or long papers, at least as summaries); if you have some to recommend, I'd appreciate it. I just think that if such very convincing material exists, you (or someone) should post it (links or even better, a topic summary/survey) on Less Wrong, such that we, a community with a high level of discourse, may discuss, debate, and examine it.