If your goal is to reduce the impact to the spine as much as possible while allowing heavy loading...
You are looking for a variety of squat that involves the torso being as vertical as possible.
Demo dude has some forwards lean and he doesn't seem able to hit legitimate depth.
You could reduce the forwards lean by:
1) Giving him a light weight to act as a counterbalance (front loaded plate squats)
If you are determined that he should be sitting his ass back behind his midfoot (rather than getting hips and ankles in vertical alignment) then he needs one of two things in order to prevent falling over backwards. A) Some degree of forward lean. B) Enough weight held out front to act as a counterbalance. The latter will help him activate his abs and keep his torso upright. Try it. Should be almost magical in its effect.
2) Improving hip mobility (goblet squat stretch)
You are right that one can't really load up the plate squat. Seems that in order to get that torso vertical and safely load the movement we are going to need to sort out his mobility issues. Need to do that anyway so he can hit legitimate depth. In order to get him sitting his ass down between his legs rather than back behind them (which we need for an upright torso - remember?) we are going to have to pry those hips open.
Just because someone can't squat is no reason to wuss out and make something easier.
Especially when your replacement exercise isn't the best at achieving the goals you have set yourself.
You just need to have a better understanding of squat mechanics so you can teach them how in a way that is safe.
Think how functional it would be (in your daily life) if you could squat down and up without weight comfortably. Chill out down there for a while. Play a couple games poker or something. Then be able to squat down and up with a heavy backpack on or something like that. With a heavy frontpack on. Holding things out in front of you. Holding them over your head. Natural, comfortable movement.
Barbells are indeed good for standardized progressive loading. The sandbag is interesting... But so are heavy rocks. Heh.