Thinking in terms of for-profit sounds like the wrong way to do it. You need to setup a 503c Foundation, much like the WMF.
Edit: it occurs to me that the Wikimedia Foundation is actually in the best position to do this! If you tried this before and still have the old infrastructure or business plan, have you considered approaching the WMF Board?
It looks interesting but a bit spooky. A real editorial board would have dozens of action editors. They only require a single review, and it's not entirely clear what the process is. They also permit rubriq, which has ill-defined measures for review quality and payment, kind of amazing given that it's wading into an area of very problematic ethics.
This doesn't feel like a major player yet, but what do I know, I'm not in medicine. In my field, reputable open journals would be things like PLOS One, JMLR, and JAIR.
Edit: it occurs to me that the Wikimedia Foundation is actually in the best position to do this! If you tried this before and still have the old infrastructure or business plan, have you considered approaching the WMF Board?