Some comments:
- the distance doesn't really matter, it's all about being in 'deep space', as indicated on the left side of your HUD. It's most conveniently found in systems with a single star, i.e. significantly above or below the plane where the planets are located. Binary or trinary systems might make it impossible to locate the 'deep space' section.
- there is a common understanding that the spawn rates increase with the population. Unfortunately, we don't have numbers on exactly how important that is
- the type of material 'high grade' USS spawn is influenced by the status and superpower alignment of the controlling faction. 'Imperial Shielding' can quite obviously be found in Empire systems - the other 'very rare' materials are sometimes not so obvious. Unfortunately, the only excellent 'USS Guide' I know of has been pulled by the author
The rest is RNG. But if you respect the above, I quite reliably find these materials within 30 mins.
I am one of those people that does produce data on this kind of thing, though I haven't done so yet, I can definitely confirm the butt-o-meter says the following...
Interesting you say there is no detailed guidance available, I might make some.
1) The number of stars in the system does not matter or change the method. The distance does matter, because you will get increased chances of other types of USS spawn when you are on the ecliptic plane. Also, below 1000ls from the main star you still get weapons fire detected, convoy dispersal etc, heavily diluting your results. Being in Deep Space AND over 1500ls above the main star, would the more accurate way to state this, just a clarification.
2) I can record some numbers and will. There are two things that assist in HGE spawns, high population and high tech industry, though industrial seems to be pretty good too. Having said that, yes you will sometimes get an agricultural system with 10k population that spits out the occasional HGE, but if you go for industrial or high tech with high populatoin (billions) you can't really go wrong.
3) Good info, yes, it's very important to understand what is LIKELY to spawn given the condition of the system you are in. For example, it's no good being in a Empire system in outbreak if you want imp shielding. While you may get a few, you will get far more Pharmaceutical Isolators. Same with Boom, you'll get more proto heat radiators and proto radiolic alloys. For CDCs (from Fed space) and Imp Shielding (from Imp Space), it is often beneficial to choose a superpower aligned system in the NONE state. This should result in a mixed bag of Imp Shielding and Proprietary composites 9 times out of 10.