Soz, I've been thinking about this. First, I think that it's not entirely appropriate for me to compare the situation you're describing with the situation I work in.
I'm paid by big corporations, and I get lots of work from them. You'd be paid by individuals, and you would likely get just a few jobs at most from one person. Since you think that this could become a steady kind of work, I think you need to establish a pay scale that's fair to you and fair to the people who hire you.
If the papers you edit are short (50 pages or less), $3-$5 a page might be reasonable. But consider whether someone would be willing or able to pay you $5 a page for a 100-page paper. $500 is a lot of money to an individual. You might consider establishing a pay scale based on a range of pages.
You also need to be clear on what you'll be expected to do. The editing I'm talking about above is copy editing. Should you have to get involved in reorganization or other big issues, you're no longer copy editing. You're doing developmental editing, which is a more time-consuming process. You should be paid more for this kind of work. I am.
As an aside, I can tell you that I've edited, reviewed, evaluated, and commented on about ten papers, books, etc. for people I know. Only once was I not criticized for the changes or suggestions I made. In a couple of cases, arguments ensued. However, in all but one instance, the people later apologized to me. (They found out I was right.) In fact, I could have done this kind of work more often, but I refused. Who needs the aggravation. I broke my own rule, and did one job recently. It was the one that did not involve any kind of criticism or arguments. Doesn't mean I'd be willing to do it. again. I'm telling you this not to discourage you. Just know that people can be mighty touchy about their writing.
That said, I think this would be a great source of work for you. I think it's a terrific opportunity. I think you'll find an appropriate and fair method for charging for your services. I wish you well.
If there's anything I can do to help or any questions you have for me, just holler.