You don't need to dig down to prevent digging. A 2 ft apron works well. Pin it down on the far edge with landscape pins and let the grass grow up through it.I have the lamp wired and latched around the leg of a ladder. The coop just needs a chicken door and im waiting for the wire cloth to come in Thursday to take out the plexiglas windows and switch out with the wire cloth. We did a 10.5x 7ft tough shed because wood is so expensive. We ended up framing the inside walls for extra support. Spanned 2 2x4s across the back wall for there roost. We are also waiting for our electric company to run power to our barn but that should be done in about a week also. The run is 10ftx25ft plus 7 feet high and they also have the deck under the coop in addition which is a 12x8. Running half inch wire cloth and dropping wire under ground 2 ft around the perimeter. My husband is actually going now to get the metal roofing panels to cover the run nowmy next question was going to be on a chicken door. Since there coop and run is predator proof should i use just a standard door?
https://www.backyardchickens.com/attachments/predator-apron-jpg.1835210/
My setup is similar. My run is as predator-proof as my coop and I never close the pop door between the two.
As soon as you get the run buttoned up and power to the coop, I'd move them out with just the brooder plate.