When I fantasize how I would make kava for large groups of people, in the hundreds plus range, I think of it like this: I'd have a cloth strainer and a pound of root in it, two gallons of water, squeeze vigorously for fifteen minutes, then start over on another pound of root with two more gallons water. I could realistically keep that up all day, provided I had enough root and water available. At 8000ml for 454g root, if 200ml is a shell, I'm making 40 shells with about ten grams root each, every fifteen minutes.
On the physics of shaking the kava, it looks like it can make a consistent brew. My challenge with shaking is I don't want to micronize my root like a rock tumbler or sharp blade blender would. I have made gentle shells before, too. I'm doing my best to be supportive here, I'm not sure how many shells you can pump out in a short time with this method. I know with large amounts of root and buckets of water I can make enough kava to meet demand, however, I am thinking incidents such as, a volley of buses full of thirsty athletes come to drink a shell together all at once, or, for a funeral, a family wants a hundred ten shells so everybody can have one at closing ceremony, or, perhaps a made-by-the-shell service for weddings and baby showers. As long as you can meet the demand and rush hours with the product, it's a success as far as I'm concerned.