True Left

The OP is an anthropocentrist, albeit a relatively well-meaning one. As some non-anthropocentrist comments correctly point out:

The logic here relies on the assumption that "evil" doesn't exist if it is not currently being perceived by humans.

That isn't an assumption that has to be accepted.

While the total violence initiated/unit time would be many orders of magnitude lower than the current total if humans all died immediately, this is not good enough:

it is bad when animals suffer while being eaten by each other in the wild. that would still happen if all humans died immediately.

We have to end this first before we can safely leave.

"But would the less competitive animals in that case not still reproduce if they are saved before we go extinct?"

They would also be prohibited from reproducing. (Reproduction itself is initiated violence, remember?)

"Of course it is more important that the more competitive bloodlines (regardless of species) should be eliminated sooner."

Actually, an alternative proposal is that if the prey species go extinct first, the predator species will follow automatically.

"should we (not myself of course as I refrain from reproduction) not still eliminate the less competitive bloodlines"

Indeed we should. Any bloodline which would not voluntarily refrain from reproducing must be prohibited from reproducing.

The sequence of steps is:

1) contain the scale of the problem (by extinction of all bloodlines which could make things worse such as by expanding into outer space);
2) maximize the trustworthiness of the antinatalists (by Aryanization);
3) controlled extinction of all non-antinatalists;
4) controlled extinction of antinatalists.

"(Would antinatalist Aryanists still need to eliminate the remaining predator bloodlines if their reproduction continues?)"

Yes. It would be part of 3).

Woke comments:

Jesus was an antinatalist.  He believed this reality was the realm of Satan but the solution (the Kingdom of Heaven being restored on Earth and evil being wiped out) would come within his disciples' generation (around 30 years).  He encouraged non-procreation until the Kingdom of Heaven arrives on Earth, which it never did.

“Daughters of Jerusalem, do not weep for me; weep for yourselves and for your children. For the days are surely coming when they will say, ‘Blessed are the barren, and the wombs that never bore, and the breasts that never nursed.’”  LUKE 23: 28–29

Fun fact: it existed among gnostics what I would call an "antinatalist prayer" that the soul had to recite when ascending to heaven:
"I have recognized myself [...] and gathered myself from every quarter, and have sown no children for the archon. But I have pulled up his roots, and gathered my scattered members, and I know who thou art. For I [...] am of the ones on high."
The heresiologist Epiphanius adds that a soul that have had children cannot be free "until it can take its
own children up and restore them to itself" (Epiphanius Panarion, 26, 13, 2).

Parents do the crime and children do the time!

While I agree with Charles Ross on antinatalism, he's a questionable authority given his animal cruelty background (he created a machine to launch unsuspecting opossums into the air as a prank).

Which proves Ross should not reproduce! (He himself still deserves to go to hell, though.)