That's interesting about the alpha being the last. Ours is also the alpha that goes in last.
One thing I forgot to mention before is I am concerned about the gaps around the access doors (by laying area and across from it) with regard to drafts. I tried towels as was suggested by someone up here, but they got wet in the rains, and may have helped cause warp in one the access doors. If anyone has a suggestion, I am all ears.
I did two things to seal the access doors on the coop.
First I made sure there were framing members to act like the door stop on a conventional door jamb. Where those members did not exist I attached trim pieces on the inside for the door to stop against.
Secondly I used V-Seal weather stripping on the nest box access door (and every other door on the coop). We used Frost King brand v-seal. If you have a particularly large gap you can put the seal strips on both the door and the jamb. Shavings do tend to accumulate in the v-seal as you use the door, which can make it hard to close. So you might have to brush them out occasionally, which is not hard to do.
I opted for flat roosts as Chickens Really recommended for frostbite concerns. They're actually 2x6 ripped in half so they're about 2.75" inches wide instead of 3.5" like a 2x4 would be. But I think it's wide enough to allow them to keep their toes warm. A flat roost also makes it easy to just rest it on cleats. That way the roost bars can be easily removed for cleaning.
Yes, a major concern is drafts, especially in our cold winters! The louvered vent is a good start. But you'll want to keep a very close eye on your girls and see how they coop is working for them. Looks like Friday night is when things are supposed to start getting really cold for us!
You really can't have too much space in the coop or run (generally speaking). You know how socked in with snow we can get! I wanted to make sure our girls wouldn't be too crowded even if they were stuck in the coop for a couple/three days. HOPEFULLY the run will remain relatively clear - ours has a rigid roof like yours. But you never know... Our coop is 4'x8' for five. I was planning on being able to house up to nine full sized hens in there, but that would be "crowded" by some people's recommendations. Our run is 10'x21'.
We attached a much-less biosecure chicken garden to our run (14'x21'). It's probably too late to do something like that this season if you wanted to expand. But hopefully it'd be a cheap and easy expansion next season if you wanted to do it
Hope some of this helps. Good luck!