I suggested before that there may be a foreign object down vent before (was known somewhere that an owner had same and found cotton bud down vent, either from previous owner trying to clean and it dropped in, or child poking it down).Sadly no sanity saved here from Cypry's post. One of my tests was to drive the car with the whole glove box removed and the rattle was still present. The rattle only occurs between 2/3 and 5/6 miles when driven from cold so it's only mildly annoying. I have checked under the gear stick gaiter and behind what used to be the ashtray for loose bits but none found.
I still think the noise comes from the HVAC unit. Maybe some more investigation next week.
Have you tried putting the blower on cold at fastest speed and opening a single vent at a time, just to see if anything makes noise or blows out?