In the following NHTSA tests higher inflation resulted in shorter braking distances, tho hyperinflation was not tested. Also worth noting the distances in most cases were only a few feet.
TIRE PRESSURE SURVEY AND TEST RESULTS
I think another forum member did some testing and found no appreciable stopping distance difference all the way up to 50psi, but I can't find it. If you've got something that says that pressures above 30psi make braking measurably worse I'd like to see it. Like really not sarcastically I'd like to see that so I know.