How does stockpile priority work?

[The Man with No Name]

I had thought that colonists would haul things to the nearest applicable stockpile and the five priority settings (Low, Normal, Preferred, Important, Critical) were for transferring things between stockpiles. However, it appears that they haul things straight to the stockpile with the highest priority. Is this right?

If so, how would one set up a chain? For example, I have a colonist making medicine in the drugs lab. There is a stockpile set to Critical for medicine in the hospital, and another one set to Low right next to his drugs lab desk. When finishing crafting a medical pack, he carries it to the hospital stockpile. Carrying single items longer distances is obviously very inefficient. How would one get him to place medicine packs in the stockpile next to him so he, or someone else, could haul multiple items at once?

[SpaceDorf]

By dropping the medicine to the ground.

The priority works thus that high priority stockpiles get filled up first, then the ones with lower priority.

Another method would be restricting your worker to a zone, that excludes the high priority stockpile.

[The Man with No Name]

By dropping the medicine to the ground.

By manually intercepting him when he's hauling every time?

[The Man with No Name]

I had also been hoping to make roofed areas next to my crop fields, so harvested crops could be dumped there, safe from the unroofed erosion penalty, and then hauled to the freezer.

[SpaceDorf]

By setting it in the Bill

Take to best Stockpile -> Drop on floor.

The arrow next to where you can set the amount.
Static Number / Forever / Do Until

[SpaceDorf]

I had also been hoping to make roofed areas next to my crop fields, so harvested crops could be dumped there, safe from the unroofed erosion penalty, and then hauled to the freezer.

That sounds like a good job for the animal squad.
Setup Zones for them and you can create a nice supply chain.

[The Man with No Name]

By setting it in the Bill

Ah, that's good. Should solve it! 

I like city-builder type games. I think the hauling system I described was used in other games, perhaps Zeus: Master of Olympus and Hearthlands. I think haulers' first priority would be to put items that weren't in a stockpile into the nearest stockpile and then, secondarily, to transfer stuff between stockpiles according to their priority setting, so it was possible to set up a chain.

That sounds like a good job for the animal squad.
Setup Zones for them and you can create a nice supply chain.

How would I do that exactly?

[SpaceDorf]

Some Animals can be trained for hauling.

Dogs, Pigs ( Wild Boars ) and some more.

Most of the time I create a animal zone for Outside Animals, Like wild boars, bears and all dirty animals.

While clean animals like dogs ( especially pregnant females ) are set to the homezone.

The outside animals can only reach your roofed food storage, while the homezone animals can reach the lower priority food storage and the kitchen storage and will haul from lower to higher priority.