I think the sheep chairs may be a bit of a gimmick and a bit of a waste of time.
I agree that turning over a sheep should not be that much of a strain, but I would also say that it does not need doing very often. I probably turn mine less that once a year, just to check their feet. Everything else is done in the race.
With big rams the best way to turn them is to pull the opposite back leg out from under them forward and into the middle. You can do this with the front leg even more effectively but they need to have something soft to land on as the come down a bit hard.