In my earlier post I didn't realize you wanted to be able to move it. That you actually want a tractor. That makes it harder.
I would consider your original tractor not horrible for four mature chickens since you are moving it regularly, maybe daily. For your six chickens it is probably too small as it is no matter how often you move it. In your climate you will not be moving it in winter.
So you want something you can move regularly in summer yet get through your winters with 6 chickens. If you remove that current "run" section that would make it hard to move that coop section so leave it, or at least the framing and the lifting handles. Removing the wire and leaving that pop door permanently locked would get rid if your access issues.
I could see cutting a new pop door on the side of that coop opposite of the nests and building a separate "run" section that can easily detached for movement. That could be a hoop coop style, maybe the wood at the ground level being 4x4 treated wood for the sides (consider them sled runners and bevel the ends to make them slide easier) and 2x4's across the front and back of this section. You should be able to move this since the hoop coop top could be pretty light. The pop door connection would be on one flat end and the human door on the other end.
The more options you want the harder it is to design for. A harsher climate doesn't help. Good luck!
When I built my tractor I had two separate 4' x 8' sections. One contained the nests and roosts and was the heaviest part but still movable. The other section had one end covered so I could keep the feed dry but was mostly covered in wire and only 24" high. Pretty light and horrible access but since I was moving it every couple of days it worked. While I moved them I could block the pop door on both sections so they could not get out. I locked them together using bolts and butterfly nuts when I wasn't moving them and let them have access to both sections 24/7. This was only for summertime. In winter I had a permanent coop and run for them. My winter climate was milder than yours and I had 8 mature chickens in that 64 square feet tractor during summer.Oh I see how it is. But we wouldn’t be able to move it about the yard. If I built that, I’d feel like the coop has to stay put.
I would consider your original tractor not horrible for four mature chickens since you are moving it regularly, maybe daily. For your six chickens it is probably too small as it is no matter how often you move it. In your climate you will not be moving it in winter.
So you want something you can move regularly in summer yet get through your winters with 6 chickens. If you remove that current "run" section that would make it hard to move that coop section so leave it, or at least the framing and the lifting handles. Removing the wire and leaving that pop door permanently locked would get rid if your access issues.
I could see cutting a new pop door on the side of that coop opposite of the nests and building a separate "run" section that can easily detached for movement. That could be a hoop coop style, maybe the wood at the ground level being 4x4 treated wood for the sides (consider them sled runners and bevel the ends to make them slide easier) and 2x4's across the front and back of this section. You should be able to move this since the hoop coop top could be pretty light. The pop door connection would be on one flat end and the human door on the other end.
The more options you want the harder it is to design for. A harsher climate doesn't help. Good luck!