I don't know if there's something for screws in wood, as wood's a rather strange material.
For bolts into steel, however, there's the AISC Manual (no prices listed, but expect it to be in the $300+ range); there used to be a separate book on joints, so you could calculate the strength based on the size of the fastener, bolt pattern, etc. There was also a section for calculating the strength of different weld patterns.
Now, the rules for the optimal strengthy are going to be similar -- further apart will support a greater moment, so when the contact patch is a square, you want the first two to be in opposing corners. If using four, fill all of the corners. However, because it's wood, you have a chance of spliting, so you don't want to go too close to the edges. (if you have to; pre-drill).
The other thing to remember is that with screws and bolts, the fasteners shouldn't be taking the full load -- they're pulling the structural material together, so that the load's transfered as friction ... this means if you see a gap between the two pieces, you need more fasteners. If you have a really large contact patch, drop another screw in the middle.
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 ;)
Best Answer
The question as clarified can be viewed as the amount of metal in the cross sections of the fasteners. The total combined cross sectional area of all the fasteners can be divided up however you want. One big screw or a dozen small screws with the same total cross sectional area will have approximately the same combined shear strength.
It isn't exactly the same because the metal isn't uniform throughout and there is variability between screws, but that is essentially the model. In this downloadable spec sheet, there is some discussion, and charts where you can compare shear strength to cross section and see the relationship. Additional discussion can be found in this downloadable reference.
It's slightly more complicated than that, though. There was a study of the shear strength of a connection for various numbers of fasteners of different types, which can be downloaded here. It looked at some established formulas for predicting shear strength based on fastener material.
It concluded that while shear strength is generally proportional to the number of screws, the formulas overestimated capacity by a small amount when the number of fasteners for the connection exceeded seven screws in low and normal ductility steels. Apparently, beyond seven fasteners, the cumulative effect of extraneous factors and statistical variations become significant. They calculated a correction factor: the estimated composite shear strength should be multiplied by a factor of 0.85 for connections with more than seven screws.
So in your example, three screws each with 1,000 lb. shear strength will have a combined shear strength of 3,000 lbs. and support a 2,000 lb. load.