So ultimately, you're making a philosophical argument that we are incapable of understanding everything. Fundamentality in physics has nothing to do with small or large processes, it has to do with the notion of what a theory encompasses. All of physics can be said to be derivable from a field theory, and that's why it is fundamental. It's got nothing to do with scale, it's got to do with the fact that nature seems to like field theory. We didn't choose to have to delve into smaller and smaller things to understand how this works, that's simply "how it is".
I don't buy that there is somehow no notion "fundamental" when you think in terms of processes. Again, this is a question of what your processes encompass. When you break down the world to the four fundamental forces, and realize that all physical actions can theoretically be derived from that, then you start to realize that you're onto something fundamental. Is there something more fundamental than these four forces that is responsible for the physics in this universe? Maybe. But as it stands, there's no reason to say there isn't, or that these processes are somehow not fundamental.
The problem I have with the reductionist accusation is that it's typically made by people who don't have a physics background, but a philosophy background. Saying that we can't know it all, that there will always be something more just out of reach, something slightly more fundamental, is tantamount to intellectually surrendering to the ephemeral nature of the physical world. Whatever is at the bottom, it is certainly not turtles, and there's no reason to think it can't be probed or understood.