Processes don't output if a single run exceeds storage

[Deantwo]

Building a warehouse for excess production doesn't seem to do anything either.

Yes, I explained that in the other thread too.

A building manufacturing commodities will always only attempt to store the commodities in its own storage. Warehouses have to fetch the commodities from the other building storages themselves, a building can't place commodities into the storage of another building.
Exception being arriving broker shipments, but they aren't actually buildings, I suspect that they are actually handled at the city level.