I am not a hiring manager, but I think at least in the Northeast, Bates has the strongest reputation and people who know LACs will know the name.
Most people on the street have only heard of a few colleges, full stop. And that is probably very regional too. Different conversation though.
I think I’ve said enough on this thread, but one more thought: OP, if you ended up being injured and unable to play your sport (which does happen), where do you think you would be happiest and have the best shot at achieving your goals? That is worth considering.