The best thing to do is to schedule meetings with those people to go over the docs with them. Now you force them to eat their own shit and waste their own time the more output they create.
I had Claude review one. It was... not complimentary. Seemed to help a bit.
Love the intent, but isn't that wishful if you don't have any leverage? e.g., the higher up will trade you for someone who doesn't cause friction or you waste too much of your own time?