Bro, it's healthcare. The coroners aren't getting paid that, the hospital is. And yes, a Google search puts it between free (for criminal cases the state is pursuing) to a few thousand dollars for private autopsies.

$3000-$10,000, depending on tests required, but in this case they would only be interested in evidence of defensive wounds or trauma caused by someone else.

I found a place in Colorado that does private autopsies for the entire continental US: https://www.postmortempath.com/

I verified they're a real business. Here's an excerpt from their FAQ:

How much does an autopsy cost?

A private autopsy generally runs between $3000 to $5000, depending on the company that you use and how many additional tests and procedures you wish to be performed.

Gosh, if only we had some sort of object at our fingertips that would let us look up information like that in an instant… perhaps something that could even let us look at several different sources to compare information…

Because the internet said so? I can't imagine it costing anything else.