MandyFitch the "nest box" is adorable. I planted my grapevines a couple years before I got chickens and built the run around them. You could either plant them on the outside of your run fencing or you'll have to protect them for a short period of time until the vines grow long enough that the chickens can't jump up and get the tip. It doesn't take much time at all before the vine will grow out of jumping height. Your local nursery will have grape vines that are relatively long--probably long enough to be too tall for the chickens.
As far as keeping chickens out of garden projects, I've found that simple welded wire works well. I took a 4' tall roll of 2" X 4" welded wire that I cut in half lengthwise so I have two strips of 2' tall fencing. I use the tag ends of the cut part in the middle to insert into the ground and don't use posts. This works best for smaller areas and areas with curves (as opposed to long straight runs), but I've never had a chicken get into anything protected by this fencing, even though it's only two feet tall (and I've never clipped wings). When crossing fences they like to fly up and land on a high point, like a top rail to the fence, before crossing over but they don't like to land and re-launch from thin wire. If you have existing fencing, you could take a foot or two of welded wire and add it to the top and that should help keep them out. I should point out that I have all heavy breeds that are less than athletic. I'm not sure how this arrangement might work for something like a leghorn or a smaller bantam.