Here are some suggestions that may help folks out.
When the BC is new, wet the strap VERY WELL - SOAK IT! - Then make the adjustments necessary to obtain a secure fit (while the strap is still wet). Once that is complete, let the BC dry. The next time you use it, it will always fit and you tank won't slip. You only have to do this once, when the BC is new. You shouldn't have to keep doing this unless you are changing tank sizes or unthreading the web strap every time you remove the tank.
To get someone's tank back in to place, get behind the diver with the loose tank. Resting the butt of the cylinder on the top of your thigh, grab the top edge of the strap and pull it down over the cylinder. The only thing encountering resistance is the tank (it's resting on your thigh). The diver, BC and everything else will move downward when you pull on the strap. This will slide the strap into position quickly and with a minimum amount of fuss. This maneuver can be done in mid-water or on the bottom.
When taking off a weight integrated BC, the trick is not to loose control of the BC. Take it off like you would a jacket, but keep a secure grip on it. Spin it around so that the tank is facing you and wrap your legs around it. Make any necessary adjustments you desire to make. With the tank still facing you, reach over the top and run your hands through the arm-holes. Lift the entire assembly over your head in a fluid motion. The water will buoy the tank, making it less heavy. The weight of the tank over your head will keep you in position. As the cylinder moves towards your back, simply guide it in position, keeping your arms as straight as possible. The tank should settle perfectly against your back without you being in danger of floating away from your equipment. The key to the entire maneuver is to simply maintain positive contact with the BC/Tank assembly.
Hope this helps.