Very interesting. My M2 does chew on the leaves and the flowers. I'd like to see the actual research on which the claims about the various parts of the euc trees are based. Are you sure there aren't any eucalyptus trees on any of the Hawaiian islands? Try a Google search on "trees of Hawaii" or something.
One claim about the "Pesto" that bothers me is this: "Chlorophyll that benefits your bird's body by improving the supply of oxygen to the circulatory system." I don't believe this. The chlorophyll molecule has the same structure (porphyrin ring) as the heme of hemoglobin molecules of red blood cells, which carry oxygen to your tissues. That's the connection they are making. As you probably know, hemoglobin carries (is built around) iron, which has a high affinity for oxygen. Chlorophyll, on the other hand, has magnesium at its center. When you eat something, including cholorophyll-rich plant material, it gets broken down in your digestive system. You aren't getting anything that's going to increase oxygen supply.
Dubious health claims like that always put me off. I wouldn't spend $40 on something like that. You can find other places that sell eucalyptus branches, and you can cut them down to foot toy size.
OK - I found some sites for you to check out. Apparently, former pineapple and sugar cane crop land is being converted to eucalyptus forest. You should be able to get "freebies" when they thin the forests. There are also probably trees growing outside of private timber industry property. Make sure you thoroughly wash anything you give to your birds, no matter where you collected it. Blue Gum in HI HI Agroforestry