The situation with the native species of Hawaii is actually much worse than most people are aware -- even people who live in Hawaii. I read somewhere[1] that, if you walk around a typical coastal town in Hawaii, and look at the lawns & gardens & parks, and watch the birds & whatnot, that you will generally not see any native species at all. The ones big enough to see are all confined to the interior.
EDIT. And, by the way, the rats weren't native, either. Hawaii has exactly two native mammals: the Hawaiian Hoary Bat and the Hawaiian Monk Seal.
[1] I think it was in Remains of a Rainbow, by D. Liittschwager & S. Middleton. https://amazon.com/dp/0792264126/
Speaking of ants that live in trees, the Big Island is being overrun by the Little Fire Ant, which has already spread across much of the rainy side. I'm sure it protects the trees from pests, too, but in this case that unfortunately also includes humans. They have a nasty bite, and are very hard to control, which is making farming in infested areas hell. http://littlefireants.com/
That's simply not true. I'm not so familiar with the fauna of Hawaii, but you can consider the moa which was happily ensconced in New Zealand for about 20 million years, and extinct within 200 years of the Polynesian settlement in the late 13th century. It's pretty clear to me in a situation like that what was native and who the invaders were, and I'd be surprised if the situation in Hawaii were very different.
New Zealand was part of Gondwanaland, and became isolated by continental drift. Anything living there when the islands became separated from the rest of the supercontinent is native.
Hawaii is a bunch of volcanoes that sprung out of the middle of the ocean. There were no land animals on the islands when they first became islands.
Now, that's a slightly topsy-turvy definition of native, which (etymologically) should mean any species that came into existence on the island.
* Indigenous - it got there without any human intervention.
* Endemic - it is not found anywhere else.
We should be thinking in terms of systems not silver bullets. Lots of farms do this and it's honestly not that hard, it just requires knowledge, process, and some diligence. But we've been defaulting toward auto-pilot agriculture for so long that it's a bit of a dramatic shift.