Your recollection of Easter Island matches exactly how Jared Diamond recounts it. Diamond also spends a lot of time considering how political organization factors in, in determining how a society responds to problems. He believed that Easter Island was fragmented into a number of autonomous kingdoms, and rivalry and competition prevented a coherent response to changing climate. Instead of adapting, the tribes tried to maintain the old lifestyle to the bitter end and fought over how to divide the shrinking pie. Diamond observes that societies with a unified political structure generally fare better, with one caveat: The leader and elite of the society must pay attention to the welfare of the society overall. When an elite hunkers down and tries to maintain a deathgrip on its own power and privilege, the society inevitably fails.
Uncomfortable lessons for the modern world, I'd say.
For some reason widespread agriculture seems to have been spotty at best. I am well aware of the numbers of farming tribes, even then many were forced to hunt. Protein is still best derived from meat. The culture would have evolved to fit each area.
Jared Diamond to the rescue...The main theme of Diamond's "Gun, Germs, and Steel" is an examination of why some societies started earlier and seemingly advanced faster than others. Diamond generally believes that the root cause is the local environment, and particularly the availability of domesticable plants and animals.
The Fertile Crescent was rich with appropriate precursors to food grains and domestic animals, so agriculture and farming began there first. In examining the Americas, Diamond notes the general lack of those precursors. The Americas had large animals, but animals that, as you note, don't lend themselves to domestication. There was a scarcity of native grains, too. The staple corn started out a miserable little pinkie-sized cob with tiny grains, and had much farther to go to become a useful food crop than the precursors to wheat and oat grains. It's not as nutritious pound-for-pound, and had to be supplemented with yams and other starchy tubers.
Given the long road to domesticate corn, it may have taken thousands of years for agriculture to gain a solid foothold in the Americas, in the regions of central Mexico and northern South America. It wasn't until about 1000 AD that corn had migrated to the northeastern and eastern United States, slowly adapting along the way to the growing conditions in northern latitudes. With agriculture coming along so late, it seems that the Native North Americans had a weakly-settled culture by the time of Columbus. Given a few more centuries the Mississippi Valley civilization would probably have become completely settled-down and might have come to equal the Aztecs and Mayas, but for one of the pillars of Diamond's thesis: Germs. We all know how that one turned out. The Mississippi Valley culture disappeared overnight, killed off by germs that preceded the white settlers, so that by the time they arrived there was little trace of that civilization.
What might have been: The Native North Americans were behind Europe by only a few centuries by the time of Columbus. Significant centuries, to be sure, with the development of sailing ships and navigation and developments in firearms; but unquestionably the NNAs were within sight of catching up, especially if the initial contacts hadn't been so disastrous and the NNAs had had time to acquire and assimilate European technology...you can't rule out the possibility that they'd have leapfrogged Europe, as has happened before when a society acquires outside technology and builds on it. A way with technology seems innately human, and what varies is the opportunity to develop and use it. Timing is everything.
Forgive me for repeating history that you probably already know better than I. I'm just building my thesis, and basically repeating what I read of Diamond. I highly recommend "Guns, Germs, and Steel" to get it from the horse's mouth.