A distinctive container for a high value treat is a great idea - I'm more likely be consistent that way.
I grew up herding dairy cows and taming youngstock by finding the pivot point between flight and not. Then leaning or raising/lowering a hand a bit (or even just eyes or shoulders depending on how untamed they were) - just enough to press in on the edge of their flight zone if I wanted them to move or ease off it if I wanted to tame them.
Chickens are more reactive than cattle but the concept works. I just need to go slower - actual speed or smaller changes in stance.
I can try both calling them and herding them to see which they respond to better.
They will be coming out these west-facing doors, going between the shed and the garden to the south of the shed, then turning into a run (not built yet) beyond the current garden fence to the east. Then back the same way.
The walls of shed and garden fence actually will it more difficult because I won't be able to get the right angle to turn them. I might have to build some hurdles or something.