Looks like you are serious about safety!
Not sure if it's too late, but if that had been me, I would have left the fence wire on the fence posts all the way to the ground, putting the bottom boards over the wire, vs. draping the wire over the boards. It may not matter enough to move it.
For sure, DO NOT bury the apron.......do it as you have done it, but only lay it flat on the ground, pinned in place with landscape fabric staples, tent stakes, etc. Trying to bury it is a ton of work you do not need to do, plus buried underground, it will rust out in no time at all. (Rusts bad enough laid flat on the ground). Once the grass grows up through it, you won't know it's there and an apron laid flat on the ground will be just as effective, if not more so.
And yes, it will be much more secure with two strands of hot wire run around the coop. One at the bottom......about the top of the bottom board.....that one for all land based predators, including dogs. And another towards the top, such that any climbing predator (coons mainly) that manages to get past the bottom wire will encounter the top hot wire while hanging on the fence wire. You can use wire or even poly rope.
Best insulators for this use would be these.........
View attachment 1323871
These create a standoff of about 5 inches or so.......goal is to get the predator to try to fit past the hot wire and fence wire. A shorter insulator too close to the fence might
a. short out, and
b. allow them to just climb over it.
Also, this has to be run using outside corners, so getting good tension on the hot wire or poly rope through the corner bend can be an issue. Put two of these insulators right on the corner and it may make the bend OK.
For a short stretch like this, you can use any of the less expensive AC fence chargers. Be careful of the really cheap Fi Shock ones. Avoid those. You want at least 5,000 volts and 7,000 is better.
Lastly, that run is awfully close to the back of your house. Not sure how many birds you plan to have, but if you get objectionable odor and flies, best solution will be 4 to 6 inches of cheap grass hay.