Would I use a reverse thread lag screw swage stud for tensioning cable

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 ;)

You must not support shelving with plasterboard anchors except when there are no other options. Plasterboard just is not that strong. It's important to locate the studs and attach the shelf supports with wood screws through the plasterboard and into the studs directly.

There are stud locators available for minimal expense, but they are not fool proof. One type works by locating the fasteners in the studs by magnetism. Since fasteners only occur intermittently, this is not the best method IMO. Another works by relative density, but is easily fooled by other masses in the wall and is confused by nearby metal. With all your power equipment, this type will not work well unless there is a section you can test that is free of confusing artefacts, such as near the floor level. You can typically assume the studs are reasonably vertical for their full length.

For determining adequate screw length into studs, I'm not sure of common UK construction practise, but you could assume most plasterworks to be from 1/2" to 1" thick. It's less critical for wood screws than plaster anchors to get the exact depth correct. For wood screws, ensure they penetrate into the stud at least 7 shank diameters depth.