I too have hilly terrain. Plus, a lot of clay. So mobile carts get really heavy, especially when its been raining.
So ive been experimenting with modular chicken tractor that so fsr is working well even on the steepest terrain.
I use galvanized (I know, a bit ick) utility panels that are 5' x 20' s 4 inch grid. I use carabeeners to connect them at each end, top and bottom. I only use two panels at a time so the run ends up the shape of a spade (think playing cards). I have cut a few 2"x2"x10' with notches that help the run stay wide, and a few 2"x2"x4' to hold up food /water containers on each end. Then I drape a mesh tarp (UV tolerant) across the top and secure that to the carabeeners as well. I used some long thin sawmill castoffs for roosting about 6" off the bottom. All in, maybe 80 USD. It works for containment and the chickens seem to feel pampered and secure.
Now the gotcha. I dont move the run exactly. I build a new one adjacent and then open the end up so they can run to the new space. Then I disasemmble the prior one and store it nearby until it again becomes the new one. At 20' long, its a two person job. At 12' it would likely be manageable for one person. I added a large plant container on its side and tossed in leaves. They use it as nesting box happily.