I don't worry about pests in my compost pile. I know that various critters live in there, not only the microherd [nice term!], but earthworms, the occasional cockroach, some pillbugs, some black soldier fly larvae, and who knows what all. They are mostly in there because they are detritovores and part of the process of breaking things down. In the case of things like aphids and thrips, [I haven't noticed them in my compost pile], they would be there because there are green plants in there that still have juices available for sucking.
In all of those cases, once the compost is finished, there is no longer any food for the critters and they go elsewhere. My finished compost never has any visible critters in it; nothing in it to feed them or keep them there.
What you do need, to be sure the finished compost is cleared out of the critters, is some time when it is sitting there without any new stuff being added. I use a two bin system, many people do three. My two bin system, every two or three months in the growing season, I take all the stuff off the top of the pile (down to the level where the earthworms are) and make it the bottom of a new pile. What's left is finished or nearly finished compost. Being exposed to the air and stirred up, it finishes up quickly and then sits there until it is used up.
If you kept adding fresh "stuff" to the finishing pile, you would keep feeding the critters.
PS fungus gnats are in there because you are keeping the pile very moist. If you want to reduce them, just let your pile dry out more. But the same thing as above applies. Once the finished compost pile dries out, they will go away.
You are working too hard at this, with all those additives!