A few seasons back I had to shoot 16 rabbits in my garden until I got the one that was chewing off beans just as they sprouted. Fifteen innocent rabbits had to die before the guilty was caught, but sometimes I believe in guilt by association. That was 16 that were actually in my garden, not just in the vicinity. So a rabbit fence would make sense. There are still plenty of rabbits in the area. The garden is 50' x 75' so about 150' of fencing. Just do it and it gets done. Right? But thinking out loud:
One problem area is my big gate, I think about 10' wide that is just wire with poles on the end that fits in loops of wire to close. Pretty basic. To stop rabbits and other things from just going under I'd have to build a better gate. My fence posts aren't able to handle that weight so I have to think about how to do that. It would probably involve putting a sill down, say a 4"x6" that juts above ground level a bit but I can drive over it, and a board along the bottom of the fence that bumps up tightly against the sill. I don't use that gate that much and the smaller pedestrian gate would be easy to fix by putting a sill down. I'd have to do something where the fence post meets the fence but that would not be too hard. Just add a bumper to the fence post (a 4x4 post) for the pole on the fence to butt against. Just use screws instead of nails to make it easy to adjust.
I use a lot of that fence to support cucumbers, Tromboncini squash, and pole beans. I have Bermuda grass, a runner grass. I'm not exactly sure how putting rabbit fencing down would affect that. Probably not a lot as far as the grass goes. I clean it up, plant the seeds, and after they sprout and start growing, put down newspaper and mulch, wrapping the newspaper up the inside of the fence some to stop the grass from coming in. For about half the area around the garden I have carper right up against the fence with wood chips on top to keep the grass down. That will take care of that half, but to stop the flat part of the fence from getting tangled with my weed eater I'd need to bury that wire a bit, say just dig up the sod, put the wire down, and put the sod back. This can be managed.
One thing about that carpet. I have to take it up every year and clean the wood chips off and replace them. They rot and form a great medium for grass and other weeds to grow in. Roots will grow through the carpet but roots can grow through the landscaping cloth I use in other places. I still have to take it up to get the rotted wood chips off and replace them. If I get that soon enough I can use it as mulch in the garden, but I usually wait so long it's filed with Bermuda roots so I use it to level the yard out, especially where the dogs have dug holes going after voles and moles.
I don't think the beans or squash would be affected, but a lot of the cucumbers form close to the bottom. If they grow inside the fencing they'll just cut themselves in two as they grow. That still happens some with my 2x4 fencing in that area but not much. I'd probably solve that by growing the cukes in the garden itself. Occasionally deer eat some of the beans growing on the outside of the fence but it usually isn't that much. I would not want to trust Bluejay's pole beans to that fence exclusively. I have planted some on it when I have some others of that same variety doing well in a protected area.
It's not just things going through the fence. I've seen a groundhog hit a fence at a full run in an area he could not have possibly gotten through that fence. Without slowing down he went under the fence. I had to look to find where he did that. Critters can squeeze through some pretty small openings. So some type of apron or burying the wire a bit is necessary to close the gaps between the ground and the bottom of the fence. To me an apron is easier than burying as long as I can keep it out of the weed eater and lawn mower.
So thinking it through the benefits probably outweigh the negatives. I may have missed something but I think all potential problems can be managed, mostly without much effort once it's in. I don't think it would make things any harder than they are now and maintenance should be minimal. So it's probably just a matter of giving it enough of a priority to get it done. How likely is that to happen. Probably not real likely to be honest. But if sixteen new rabbits show up in the garden itself it may become a priority. Funny how priorities change.
I too believe in guilty by association. 
Love your plans, Major, and would love to see a pic or two of it all when you are done. 
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