It's difficult to model the situation with rational analysis, there's too many intangible factors. You could do an empirical test. You need to support 20 lbs per fastener. We can apply a safety factor of 3 for ultimate strength, so the fastener should support 60 lbs without actually breaking. So you would need 2-4 fasteners to support your weight. Round down to the closest whole number. Install the clips as you did in the wall, except now install a metal strap between the screw head and clip. Arrange the straps so you can step into them to weight the system. Arrange the straps such that your weight is distributed evenly to each fastener.
Weight the system and see if they break. If you live in a seismic area, bounce on them a bit and see if they break. You'll either be able to sleep better or you'll know what to do next, depending on the outcome. Obviously there are better ways to set up an empirical test, I chose to illustrate a quick and dirty method just as an example. Be sure you are protected from flying shards of metal.
Regarding an increaser for the number of fasteners. No, you can't do that. It is a valid concept though, for example you can use a higher allowable bending stress in multiple floor joists than you can in a single use situation such as a header. The concept is not generally applied to fasteners.
Response to OP's Update
Shear strength in relation to fasteners partly depends on what the fastener is holding. In this case it's known as a metal side plate condition, meaning the expected failure mode will either be the top of the screw failing through the shank (shear) or the wood collapsing under the compression from the screw. It's rare in reality to have a perfect shear condition, there is usually some bending and tension components as well.
A true shear condition would something like a metal strap screwed to the wood surface and all the force was parallel to the wood surface, exactly perpendicular to the screw shank. In your test, you mostly have the vertical shear component, but there is a tension component as the center of mass is away from the wall surface. We can safely ignore the tension component in calculating a working load since 80# in pure shear is more conservative than 80# shear and, oh... say 15# tension combined.
A picture of the clip was helpful, I imagined a much worse condition. Either way, the ultimate strength will not be proportional to shear alone, there are other factors difficult to model, thus testing is the best approach. The failure mode you experienced is a bending failure, but your actual installation, while having a bending component, is in fact mostly a shear condition.
The duration of load is a factor. The usual allowable stresses specified in construction are for permanently applied loads. The allowable stresses can be increased for shorter durations, 15% for a few months, 25% for a few weeks, 33% for a few minutes. Meaning we should reduce the allowable load determined through short term tests accordingly. But we also don't know the ultimate load since you didn't achieve failure. Just as well, uncontrolled destructive testing can be a little too exciting. You also haven't run multiple tests (I assume) to confirm you are getting consistent results.
Let's say you did run multiple tests and they all actually failed at 80#. When you apply the 3x safety factor, then adjust for duration of load, you end up with a working load of 20#, exactly what you need. Considering there was no failure experienced, and the installation does appear to be predominantly shear, I think your installation is safe. Barely. Next time around, use heavy ordinary wood screws ;)
The paper is a key part of the drywall structure. Just as when you cut the paper on the drywall it's easy to snap, when you screw past the paper it's easy to blow out the back. Plaster and paper are a lot like concrete and rebar, the plaster based core of drywall resists compression, while the paper resists tension.
It's not essential to pull the old screws, the damage has already been done and will be mudded over. But you should add a second screw a few inches away anywhere you went too deep. This is a critical repair for drywall on the ceiling, and a very good idea for drywall mounted on the wall. I wouldn't go through any added effort to tear down the drywall, since it's still perfectly good. Just add the extra screws and be happy you caught the problem before experiencing a collapse.
Update: From your new photos, those screws are too deep. Once the paper has been torn, you lose strength at that screw location. You should never be able to see plaster around the screw head, but you also should never be able to run a flat edge over the drywall and feel the screw head above the drywall. It's a fine line to walk, but a professional drywaller should be able to walk it with ease (we train amateurs to do this in under a hour).
Also, from those photos, it doesn't appear that the installers are using a drywall bit (we refer to them as mushroom bits because of their shape). They leave a distinct ring around each screw, making it easy to countersink the proper depth, and preventing you from going deeper (the bit will cam out when it hits the paper).
Best Answer
Dampening and scoring the back paper is the right way to prepare drywall for installation around a curve. A quick back-of-the-envelope calculation says that the radius of curvature was about 30", which should have been OK (my drywall book says 20" minimum for 1/2" panels). You may simply have been unlucky with it breaking.
There are flexible drywall panels, though I've never seen them in the stores. Failing that, you could also try a double thickness of 1/4" panels, which are widely available.