Thanks for the feedback and discussion. After reading through your thoughts and thinking on things a bit, I realized a third option.
Part of 1.4 is a rework of settlement production logic. Instead of creating items as needed, with the player able to optionally set a target surplus, settlements now try to keep a buffer of inputs and outputs.
As an example: a Brickworks can produce 2 mudbrick in 15 turns, a 150 turn buffer of outputs is 10 mudbrick. So for each Brickworks the settlement tries to keep 10 mudbrick in storage.
The goal of this was to make calculations for automatic trading easier. A side effect is that, when an item is needed, it's most likely already in a storehouse. This fact changes the logistical situation. Instead of optimizing for efficient gathering of items, we can optimize around efficient sending of items.
So, with that in mind, I think the solution could be rather simple. Define a new type of upgrade for some structures. Each level of this upgrade makes a handcart available in that structure. When a citizen picks up items to carry, if there is a handcart available they can claim it, and use it to carry multiple shipments at once.
I think Option 2 might be a good idea for an advanced option later. Perhaps related around defining "districts" in a large city, with each acting like an independent settlement with regards to citizen and item distribution.