OK.
Why does this matter? Regardless of the origin of an idea, it needn’t be anyone else’s motivation for adopting the position (in particular, it’s not my motivation or goal in taking this position).
I don’t follow your intent here. The statement “‘Objective should’ does not correspond to any meaningful concept” is not itself a statement of obligation, so why ask in what sense one is obligated to act in accordance with it? Similarly if I said, “‘Pzqpqqt’ is meaningless,” what would it mean to be “obligated to act in accordance” with that statement (or its negation)?
What obligation? Not all propositional statements are statements of obligation.
Again, where’s the obligation for the non-cognitivist (which, by the way, is not precisely my meta-ethical position)?