Hey there,
I would skip the tpost strand idea. More work expense and may not work as well as you would hope.
You could attach the insulators directly to coop and run, quick and easy. It will save money, and might avoid a big pain making and using a gate.
****Also, strand electric must have a second barrier visible to the critter (they don't get to touch it, so it doesnt have to be sturdy, but they need to NOT be able to figure out they can skip through the wires to open ground (see raccoon and foxes in the vineyard) earlier.
Also. I have a 10 by 10 chain link, electrified. I bought the smallest charger and the electric jumps on a wire to the pen about 30 feet, wraps around twice.....even the gate which is only wired connected through the handle gets 5000 on the meter. You are not fencing miles ...
My coon hound hit it months ago and will still not go into the back yard.
(SO bought the "big charger", we have the same output, just sayin.)
As others said, strand down low, to deter diggers, about 7 inches higher for nosers.....up to as many as you wish. If you feel that something can avoid the lower wires by jumping or climbing, a strand of hot plus a strand of ground near the top, close enough so they touch both at the same time. FYI - raccoons are not known to jump up onto something.
-A
p.s. fox tracks and possum tracks in the snow travelling within a few feet f the run, do not even stop to investigate. Good these are trained

. IT works.