I have been wanting to do your gapper program for over a year but I haven't thought seriously about doing it because I have a dog that I love dearly.
I am writing this because, as someone who only knows the terrain of Wheaton Labs from pictures, I'm not sure what to expect so I can can present my thoughts on an ideal situation as a dog owner without the constraint of preconceived notions about what is and is not available.
A good situation for me and my dog would be one where we live in a small cabin or tiny home where I could leave him during the day, but where I could check in on him during the day during breaks.
Obviously exercise is necessary for dogs and he loves hiking off leash, but I am always conscious that some people do not like dogs or are afraid of dogs so if he needed to be leashed the entire time we would both be ok with that for walks. I think this is true for a lot of dogs except high energy working dogs.
My dog likes to run a bit and usually does this in our back yard or a dog park by retrieving a ball so a dog run would be good for that, but always with my supervision.
He likes dogs and people but is shy with people and backs away if they try to reach for him too fast. He usually goes in the small dog run because large dogs tend to chase and tackle him. This is why my supervision of my dog is necessary, because I have had other dog owners say I am overreacting when their dog is pouncing on mine which I am not and they don't know my dog and when he is unhappy which I can see immediately.
He stays with a dog sitter that watches up to 8 dogs at a time but she makes sure that they are all chill dogs that have compatible personalities. I trust her to know how to facilitate this group in a healthy, safe way.
He does not chase animals... not even the squirrels or rabbits that come into our yard. I have trained that out of him because it is dangerous in suburbia as they have a tendency to randomly run into the street. But I could see how this could be a problem on a farm. Maybe making the dog take a test of verbal commands as a rule of acceptance into the "pack" on your land.
Finally, I would definitely go for a week or so without my dog to check out the program, the land, living space, the vibe to make sure that it would work for everyone involved. It is much easier to tell how things will go once I am physically there then by only doing research on the Internet. I feel like requiring the dog owner to see the life at Wheaton Labs would be a a good thing.
What is really UNAPPEALING about how you have presented the dog situation is that it seems like some nut with a gun could shoot my dog if my dog (my best friend, by the way) gets too close to the chicken coop, even if he is just peeing or whatever. Again, he doesn't chase animals and he's been around chickens and wild turkeys. Generally, he's afraid of other animals except for dogs. Even cats. (And I'm using the term "nut" at this point because I don't know who this person is and my opinion will probably change if/when I meet him, just like you probably see the potential of a dog being vicious animal killers until you meet it).
The fact that he could get shot for straying terrifies me and makes me want to wait a decade until I do not have a dog to even think about visiting Wheaton Labs. Sorry, but that's my honest opinion. This saddens me because I feel like you guys are on the cutting edge of permaculture and that the need for this technology in the world is so important to learn and use and share. And you guys lose out, too, because I actually am a good worker who would be very content to peel bark off trees or build fences and make tools (as described in your podcast) and I already have my PDC, so I understand what you are doing to a certain extent. And I'm sure there are other people like me that would love to be part of your community but are held back by the dog issue.
Anyway, I hope this helps in helping you to create a comfortable and safe space for dogs, their owners and all other inhabitants on your land.