I don't know, it seems kind of dangerous, granting Constitutional authority to an extra-Constitutional agency. That sounds like an end-run around the checks-and-balances established by the Founders when they drafted the Constitution. Obama’s “Czars” were questionable on similar grounds. Having persons or agencies unaccountable to the electorate exercising powers reserved by the Constitution to persons or agencies who are accountable seems a de facto veto by the Executive of powers heretofore reserved to another branch of government. I would then invoke the Separation clause as well as the Commerce clause in challenging the constitutionality of the action.
I agree with you on this, and it really goes back to a series of decisions the Supreme Court made decades ago regarding these administrative agencies. Scalia once famously labelled the U.S. Sentencing Commission as sort of a "junior-varsity Congress" because it had been given authority that should be Congress' alone. You could google "Mistretta" (the name of that case) and read his entire entertaining rant on the subject.
In any case, I wasn't trying to open that can of worms here. I was simply trying to point out the legal power of the NLRB, and what it meant in this particular situation.