This is an interesting question, but I'm not sure if there's really a canonical answer to it yet. I don't think I've even seen the beginnings of discussion about it. You might have to go to the actual Google support lists for anything like resolution, assuming an employee decides to take the question on.
rel-me has always been about people, back to 2003-ish. Since you mention product pages, I'm assuming you're asking about using this on something like a shopping site. Entities like stores and companies just plain aren't in the conceptual framework of XFN.
Also keep in mind that at the time of Google's announcement(June 2011), only people could have Google/+ profiles to point back at with the rel-me link, anyway(we'll ignore the cheaters here). Brand/company pages didn't happen until November. So besides what you're asking about being fundamentally outside the intended scope of rel-me, it wouldn't even have been part of the discussion at the time.
In practical terms, there's nothing technically keeping you from adding markup to your site saying the author is "Tchalvak's Widget Co" and pointing at your company's Google profile. It might even work, and it does make a certain amount of sense, though people might view it as a little odd. If Google has a problem with it, I'm sure they'll just quash brand profiles from appearing as author snippets and maybe eventually handle it properly. Unfortunately, I can't immediately recall if I've seen a brand already do this, as proof of concept. For the time being, since you say it'd be a lot of effort, I'd recommend skipping it unless you can get a real answer out of Google.