Enduser's advice sounds good to me. Perhaps start off with a pesticide, if that doesn't kill the critters, try something stronger. The copper makes sense since your tree has anthracnose.
Why would I want to kill something I haven't yet identified? Even after identifying it, why would be first choice be to use a pesticide? Why not let the other bugs handle it. Mango trees are pretty good at taking care of themselves. I don't think I have ever had to spray a pesticide on any mango tree I've planted in the ground.
The reason the copper doesn't make sense to me is that over use of copper can be damaging to the environment and unless my tree is flowering and I am possibly going to lose a large amount of fruit I see no need to spray copper on my tree.
I agree with you on no heavy dose of pesticide for your tree. Like you said, better to first find out what they are as it doesn't seem to be causing any damage at the moment.
As for copper, if you are having major anthracnose issues or some other invasive fungal issues I would attack with a strong regime of copper. Otherwise, once a month or even once every other month should more than suffice. if you had fruit to "protect", that would be different.