Stationary Coop- Moveable Run (Modified Paddock System)-Will it work??

Hello everyone! We are first time chicken owners and we are completing the design for our coop. We have been looking at the different options for chicken coop set up and what would work for our yard. Here is some information:

1. We live in the city on a .75 acre lot with seven chickens.
2. Our backyard is split up into terraces so we do not have a lot of flexibility for dimensions. Our largest terrace is 50 ft x 18ft.
3. It is important to us that our chickens are able to forage but in an enclosed space (close neighbors, predators), but we also understand how quickly chickens can eat up grass.

Right now, we are considering two options: chicken tractor or a coop with a paddock system.

We like that the chicken tractor is simple to build and we can move it around in our yard. Cons: they tend to be so small that the run couldn't be as big as we'd like it to be (not enough room for chickens to be comfortable and the grass gets depleted more quickly). The coop wouldn't be as secure either and not as good for our cold climate.

We are attracted to the paddock system because we would be able to do the deep litter method with a stationary coop and the chickens would be able to eat vegetation without depleting a whole area. For us, the cons of the paddock system is that it requires a lot of different fencing and surface area on our small-ish city lot.

We are wondering if it is possible to have a stationary coop with an attachable run that could be attached to three of the coop's walls (creating three paddocks). While we have seen many paddock systems with four paddocks, the combination of terraces and a rotational run limits it to three. The coop would be 6 x 6 and the run would be 6x12. I have attached a visual to this post. Since the run is so large, we would either make the run out of PVC pipe or put wheels at the end of it for easier mobility.

Since we are new chicken owners, we wanted to consult you seasoned veterans out there about the design, as there are probably things we hadn't thought about. We also have a few questions:

1. Anyone have ideas about how to make the run easy to move around? Particular materials or modifications?
2. Any ideas on how to attach and detach the run from the coop walls?
3. Would three 70 sq ft paddocks be enough vegetation for seven chickens if we moved it weekly?
4. This terrace is particularly shaded so while it grows grass, it doesn't grow quite as quickly. Can that be alleviated with grass seed?
5. Is there some sort of chicken tractor design that is big enough for foraging but easy enough to carry around the yard?