Actually, let’s just use some the same logic that courts have just accepted to force gay marriage on us all. DOMA meant that the states had delegated the right to regulate marriage the Feds, so the Feds could decide what marriage meant.
The National Labor Relations Board, therefore, means that the states have delegated regulation of labor unions to the Feds.
Alternately: Labor unions are almost always inter-state organizations and the manufacturing sector unions make things intended for sale inter-state. Therefore, the Interstate Commerce clause can be used to regulate them.
Either way, problem solved.
Interesting line of thought. Courts have been known to pick up such novel lines of reasoning.