Now I know that's conclusory, and just a recitation of my point, but perhaps my response to the rest will help ...
This isn't "washing my hands of an ugly situation;" it's precisely the opposite. I don't want to remove illegal immigrants. I don't want to close down shops.
I want to give illegal immigrants [at least some] rights and a path to citizenship. I want "sweat shops" to become "UDHR-compliant shops" (sadly, not the same ring to it). That's the "lifting the floor" I referred to.
Your question is virtually impossible to answer (for instance, who am I?) ... Would I force a company operating a "sweat shop" to raise its standards? Hell yes. We've done that in America. Would I prevent "sweat shops" from opening? Hell yes. Would I prevent a company from opening a shop that pays its workers incredibly meager sums? Not necessarily.
I understand your implicit point about the jobs flowing to the country of the next least resistance, the next biggest human rights offender. That's a practical issue and a huge one. But that doesn't mean we just throw up our hands, does it?
As for "who is better off?" ... First, workers would have rights, both in name and in reality. And benefits flow beyond just those directly affected. An increased legal status and better legal protection for my neighbor validates my legal status and my legal protection. Otherwise, ****, what do I have? If a MNE can disenfranchise Cambodians, why can't it disenfranchise me?