Your points (1) and (2) seem like fully general counterarguments against any activity at all, other than the single most effective activity at any given time.

That's more or less what I intended them to be. Isn't doing only the most effective activities available to you... a good idea?

However, I'd phrase the argument in terms of degrees: Activities are good to the extent they conduce to your making better decisions for the future, bad to the extent they conduce to your making worse decisions for the future. So doing the dishes might be OK even if it's not the Single Best Thing You Could Possibly Be Doing Right Now, provided it indirectly helps you do better things than you otherwise would. Some suboptimal things are more suboptimal than others.

However, it seems that one of the best ways to do that is to encourage others to care more for the welfare of non-human animals

Maybe? If you could give such an argument, though, it would show that my argument isn't a fully general counterargument -- vegetarianism would be an exception, precisely because it would be the optimal decision.

it makes sense from a psychological perspective to become a veg*an if you care about non-human animals.

Right. I think the disagreement is about the ethical character of vegetarianism, not about whether it's a psychologically or aesthetically appealing life-decision (to some people). It's possible to care about the wrong things, and it's possible to assign moral weight to things that don't deserve it. Ghosts, blastocysts, broccoli stalks, abstract objects....

Although I see no way to falsify this belief, I also don't see any reason to believe that it's true.

To assess (4) I think we'd need to look at the broader ethical and neurological theories that entail it, and assess the evidence for and against them. This is a big project. Personally, my uncertainty about the moral character of non-sapients is very large, though I think I lean in your direction. (Actually, my uncertainty and confusion about most things sapience- and sentience- related are very large.)