Oh yeah, just a thought . . .
You've had several.
The line about how weapons training is supposed to inform your empty-hand practice is, unfortunately, a bit of a platitude much of the time. That is, it's true, but it's also something that people repeat without really thinking about, much less seeing the connection to what they're doing. It's like an old Bill Cosby joke in which kids in kindergarten are taught that one and one is two. Kid's reaction: "One and one is two! Great, that's amazing, yes sirree...what's a two?"
So, it seems to me that weapons training can only inform your empty-hand training by starting with martially effective/valid weapons techniques, and then going from there. If instead you have a situation where people are told to pick up this wooden thing, and then they're told the line about how it's supposed to inform their body art, most likely they'll try to make motions that mimic what they think they're supposed to be doing in body art, only now they're holding this stick. IMO, this is exactly backwards.