Definitely consider burying your fence. I also went with welded wire for all my runs and buried it about 12" deep (mainly because I wasn't so good with the trencher to keep it at a steady 8" depth! hehe) Then all along the perimeter we have the electric fence wire. My only concern is making sure that the kids (4 & 2) don't touch the fence, but I think we've instilled the fear of god in them about that one, so they keep a wide berth.
There are plenty of critters out here that would love to get in, but that combo has kept everyone out. The fact that they kicked the door in though...whoa. What kind of door are you going with for the redesigned coop?
Sorry for your loss. We have electric fence plus barb wire three strands high around the bottom of our chicken coop and run. Plus my husband put lights in the run area that come on at dark. I don't think the fox and coyote we have here want to come into the light and get electrocuted.