The main potential stability issue is when lifting or lowering the car. Just like when lowering the car without the liftbars, if the trolley jack can't slide on the concrete (for instance if it's on really rough asphalt), the car can shift laterally as it's lowered. As far as I can tell, if you were to use these on reasonably smooth concrete where the jack can roll without obstruction, there should be very minimal risk of the lift bars rolling out of position. Most trolley jacks have a slightly recessed "cross" in the actual jacking circle which fits right into the liftbar and would prevent it from sliding off.
Once the car is up on both lift bars, it is rock stable.
Ken does recommend lifting one side to the minimum height of the jackstands - then the other side to the minimum - then going back to the first side and resettling the jackstands to make sure the weight is evenly distributed. Then raising higher than the minimum on each side if needed.
The only modification Ken mentioned is going to be reducing the amount of clearance with the plastic rocker covers. This prototype has about 1 cm more clearance than needed.
To me, these seem super usable. They standardize the process of jacking and stabilizing the car and reduce the risk of human error causing a failure. I was considering a quickjack but I think I prefer the liftbars as they provide a lot more access under the car, are super easy to store, and are, of course, much less expensive.