I will note, I have been trying to think of other things that could help alleviate this problem of droids getting stuck. I do have one idea, but I'm not sure it would go with your intended design.
My suggestion would be that the starting warehouses are all one huge warehouse with four entrances on one side and four exits on the other. When a droid is making the journey back to the warehouse to either deliver or pick up a material, once it's a set distance away from the warehouse it will be assigned to whatever entrance door has gone the longest without being assigned (with the first times being down the line of doors). Since the droids would always be going straight through, they technically should never have a singular jam (which I have seen happen usually when they're trying to exit. I even saw this in the new prototype at speed x1 D: ). Meanwhile, by assigning the door once it hits a specific range, it should ensure that no two droids will reach the same door at the same time since if two droids hit that range about the same time, they should be assigned different doors (mind you, I do realize it's possible, though likely very rare, that two droids could hit the range at the exact same time. I think the solution there would be to randomly select which one to set first). Now if any jams happen, it should be outside of the warehouse by these doors rather than inside.
I'm not as familiar with the Godot engine as I'd like to be, so you'd be the one who could tell me if all of this was doable.
If you need anymore input/feedback or even want help testing, feel free to hit me up. I'll link both Twitter and Facebook pages for you (since it may take me longer to notice stuff on itch).