You don't need to go down with your apron. Go horizontal. Pin the outer edge with landscape pins, cover with sod and seed. Check out the link to My Coop build (under my information in my avatar) for pictures of what I'm talking about.I'm limited to 144 square feet total, by village guidelines. My plan is 8' x 18', coop for the first 6', and run for the rest. A storage closet on the side of the coop will reduce the coop size to 6' x 6', raised 2' off the ground.
I'm planning a predator apron as deep as I can get it, covering everything with hardware cloth, and a full roof over the run to keep snow and rain out to some extent.
I'm thinking I will make a PVC pipe feeder that fills from the storage closet, and sits under the coop, where it's more sheltered than the rest of the run.
This is my first year in NY, (I'm from Utah), so no experience with the climate here. I've heard from locals that wind is really an issue in the winter, so I'm planning to make panels to place on the outside of the run to provide wind breaks when needed.
That's the plan right now. I've drawn and redrawn plans about six different ways over the last month. Hoping to start building next month, depending on the weather. Might have to build in segments in the garage, and then assemble outside later if we get a lot of snow soon. Don't want to be caught with no coop when spring gets here!
You are starting with a footprint that offers 24 sq ft per bird so that's fantastic!
I also advise building a walk-in style coop. I've had both raised and walk-in and would never do raised again. It's nearly impossible to fetch a chicken at roost to tend to it or do routine health checks when you can't get in the coop yourself. Accessing the area under the coop can be a real pain too.