We're treading close to terminal values here. I will express some aesthetic preference for nature qua nature.

That strikes me as inconsistent, assuming that preventing suffering/minimizing disutility is also a terminal value. In those terms, nature is bad. Really, really bad.

I also recognize a libertarian attitude that we should allow other individuals to live the lives they choose in the environments they find themselves to the extent reasonably possible.

It seems arbitrary to exclude the environment from the cluster of factors that go into living "the lives they choose." I choose to not live in a hostile environment where things much larger than me are trying to flay me alive, and I don't think it's too much of a stretch to assume that most other conscious beings would choose the same if they knew they had the option.

Absent strong reasons otherwise, "do no harm" and "careful, limited action" should be the default position. The best we can do for animals that don't have several millennia of adaptation to human companionship (i.e. not dogs, cats, and horses) is to leave them alone and not destroy their natural habitat.

Taken with this...

We need to value the species as a whole, not just the individual members; and we need to value their inherent nature as predators and prey.

...it seems like you don't really have a problem with animal suffering, as long as human beings aren't the ones causing it. But the gazelle doesn't really care whether she's being chased down by a bowhunter or a lion, although she might arguably prefer that the human kill her if she knew what was in store for her from the lion.

I still don't know why you think we ought to value predators' "inherent nature" as predators or treat entire species as more important than their constituent individuals. My follow-up questions would be:

(1) If there were a species of animal who fed on the chemicals produced from intense, prolonged suffering and fear, would we be right to value its "inherent nature" as a torturer? Would it not be justifiable to either destroy it or alter it sufficiently that it didn't need to torture other creatures to eat?

(2) What is the value in keeping any given species in existence, assuming that its disappearance would have an immense positive effect on the other conscious beings in its environment? Why is having n species necessarily better than having n-1? Presumably, you wouldn't want to add the torture-predators in the question above to our ecosystem - but if they were already here, would you want them to continue existing? Are worlds in which they exist somehow better than ours?

We have neither the knowledge nor the will to protect individual, non-pet animals.

We certainly know enough to be able to cure their most common ailments, ease their physical pain, and prevent them from dying from the sort of injuries and illnesses that would finish them off in their natural environments. Our knowledge isn't perfect, but it's a stretch to say we don't have "the knowledge to protect" them. I suspect that our will to do so is constrained by the scope of the problem. "Fixing nature" is too big a task to wrap our heads around - for now. That might not always be the case.

When you ask, "Assuming that these environments are (or would be) on the whole substantially better on the measures that matter to the individual living in them, why shouldn't we?" it's not clear to me whether you're referring to why we shouldn't move humans into virtual boxes or why we shouldn't move animals into virtual boxes, or both.

Both.

If you're talking about humans, the answer is because we don't get to make that choice for other humans. I for one have no desire to live my life in Nozick box, and will oppose anyone who tries to put me in one while I'm still capable of living a normal life.

Then that environment wouldn't be better on the measures that matter to you, although I suspect that there is some plausible virtual box sufficiently better on the other measures that you would prefer it to the box you live in now. I have a hard time understanding what is so unappealing about a virtual world versus the "real one."

If you're referring to animals, the argument is similar though more indirect. Ultimately humans should not take it upon themselves to decide how another species lives.

This suggests to me that you haven't really internalized exactly how bad it is to be chased down by something that wants to pin you down and eat parts of you away until you finally die.

The burden of proof rests on those who wish to tamper with nature, not those who wish to leave it alone.

To prove what?