Thank you for continuing to engage with this topic.

Let me break down your argument.

Premise 1a: "The only people who want an independent investigation are people that believe Sandy Hook was a hoax."

I do not believe that Sandy Hook was a hoax, but I still support the ability of citizens in a democracy to independently investigate matters being used by the government to shape its legal framework. This is particularly important in constitutional challenges.

Premise 1b: "No parent or family has come out and said they do not believe what the cops found in their investigation.

This part is not relevant. Despite the families of victims' being one group of stakeholders with presumably a high interest in knowing the truth, the fact that we don't know of any who have wanted better evidence does not mean that the evidence is good enough for other people. There is a vast gap between those who suffered loss and "hoax believing conspiracy theorists" that includes reasonable people with many points of view. If I approached any group of investigators, private or public, and said that they should not look into a matter because of my personal connection to it, they would rightly tell me to fuck right off.

P2: Any investigation would have to rely a lot on what the state police collected.

Yes, many years after the fact, that is certainly the case, and even a fresh case would surely borrow from the official policework. I believe the counterargument is that people be given concrete evidence that does not rely upon opinions or official reports.

Conclusion: Tho[s]e hoax believers say the state police was part of the hoax, would they believe in the evidence the state police give them?

This fails because a) the aim is not to convince a small group of people who won't listen to reason and b) there are people want evidence outside the scope of what is easily manipulated by the police. Would you accept the argument that some people will never believe outer space exists, so we should not conduct astronomy outside of NASA?