Follow the link in my signature below. I don't believe in those magic numbers for square footage you often read on here, that article may tell you why. For some people those magic numbers are overkill but for some they are not enough. In your southeast Missouri weather your chickens will probably be able to be outside all day practically every day so they probably won't be confined to that coop a lot. I find that the more I crowd them the more behavioral problems I have to deal with, the harder I have to work, and the less flexibility I have to deal with issues. I consider my comfort and time important considerations.
To me flexibility is the most important. An example. Say a fox starts picking off one chicken a day. This happened to Dad. Foxes can be hard to deal with, may take time. What do you do while you are dealing with that fox, continue to lose one a day? As a minimum I'd want a good predator proof run if your coop is too small to lock them up for several days.
With that many chickens, absolutely. And you need enough room to work in there.
People don't complain about having too big a coop, they complain about it being too small.
Then why are you worried about building it a bit bigger? Why go out of your way to create potential problems? Granted, foundations and roofing cost a lot, as well as siding.
If you were buying the material, most building materials come n standard sizes, usually 4' and 8'. Not just lumber but paneling and plywood. If you can design around that you can often reduce cutting and waste and get something a bit bigger at no real extra cost. If you already have material design to those dimensions.
You can use shed plans. Home Depot or Lowe's sometimes sell shed designs. You may be able to find shed plans at your local library. If you look at the top of this page under the Articles tab you will find a section on coops. Many of those come with plans. That's the first place I'd look, see if you can fine something that suits you.