Before I begin, for the most part, HGE (High Grade Emissions), have too many levels of RNG.
The diagram below is what it takes to find one drop of the correct G5 manufactured material.
The yellow loop is what people do to avoid this. Lol
As you can see, you need to pass six checks to get one G5 drop. Failing any of those means you either get nothing, or something else, and must start all over again.
My first suggestion is unlink the major and minor faction from the list of things to be correct, and make it so only the minor factions state is what governs what's inside the HGE.
For example, if the HGE says "outbreak", then you can be sure that the contents will be something from the chemical line of manufactured materials, and hopefully from Pharmaceutical Isolators.
For manufactured materials from major factions at war/civil war (Core Dynamic Composites and Imperial Shielding), if the HGE is owned by a faction aligned to a major faction, then spawn something from Composite (Federation) or Shielding (Imperial) lines inside the HGEs. If the faction is Independent, spawn something from the Thermic line (Military Grade Alloys), or Alliance spawn something from the Capacitors line (Military Supercapacitors).
4 major factions at war/civil war, for 4 manufactured groups. Makes sense.
A two G5 manufactured materials (Proto Radiolic Alloys, and Proto Heat Radiators) are both reliant on the Boom state, these should be separated, so 1 replies on Boom, the other on Bust (or something else entirely)
Other G5's are simply not available from anything other than missions.
With plenty of new faction states to play with, these could be assigned to drop from any number of the new states.
Exquisite Focus Crystals and Biotech Conductors, for example, can spawn from states such as Elated, Bust, Expansion or Retreat, and so on.
Or, alternatively a complete overhaul of the HGE spawning system, could use the rarer states as the governing factor for how sought after some G5 materials are, but making sure that those HGEs now contain what you're looking for.
FD knows which states show up less often, and which materials are most sought after, so this should be fairly straightforward.
All that really matters, is if you find the correctly labelled HGE, it should contain material line as stated in the items description.
So a signal source, labelled as "outbreak", in an outbreak system, will contain materials from the chemical line, and higher grade signal sources will be more likely to contain Pharmaceutical Isolators.
As a final note, material traders are a good back up, but it's very frustrating to simply never find what you're looking for, and instead grind up six times as many materials that will spawn, just to trade them in. If you need a lot of say, Military Supercapacitors, which are usually used in weapons, which you usually use more than 1 of, it means you'll need maybe 20-30 of these, this would be 2-3 correct HGEs.
Or 12-18 incorrect ones.
And if you happen to need those "incorrect" materials for something else as well, then you need to visit even more HGEs, as well as frequent visits to traders to make sure you're not too full.
The diagram below is what it takes to find one drop of the correct G5 manufactured material.

The yellow loop is what people do to avoid this. Lol
As you can see, you need to pass six checks to get one G5 drop. Failing any of those means you either get nothing, or something else, and must start all over again.
My first suggestion is unlink the major and minor faction from the list of things to be correct, and make it so only the minor factions state is what governs what's inside the HGE.
For example, if the HGE says "outbreak", then you can be sure that the contents will be something from the chemical line of manufactured materials, and hopefully from Pharmaceutical Isolators.
For manufactured materials from major factions at war/civil war (Core Dynamic Composites and Imperial Shielding), if the HGE is owned by a faction aligned to a major faction, then spawn something from Composite (Federation) or Shielding (Imperial) lines inside the HGEs. If the faction is Independent, spawn something from the Thermic line (Military Grade Alloys), or Alliance spawn something from the Capacitors line (Military Supercapacitors).
4 major factions at war/civil war, for 4 manufactured groups. Makes sense.
A two G5 manufactured materials (Proto Radiolic Alloys, and Proto Heat Radiators) are both reliant on the Boom state, these should be separated, so 1 replies on Boom, the other on Bust (or something else entirely)
Other G5's are simply not available from anything other than missions.
With plenty of new faction states to play with, these could be assigned to drop from any number of the new states.
Exquisite Focus Crystals and Biotech Conductors, for example, can spawn from states such as Elated, Bust, Expansion or Retreat, and so on.
Or, alternatively a complete overhaul of the HGE spawning system, could use the rarer states as the governing factor for how sought after some G5 materials are, but making sure that those HGEs now contain what you're looking for.
FD knows which states show up less often, and which materials are most sought after, so this should be fairly straightforward.
All that really matters, is if you find the correctly labelled HGE, it should contain material line as stated in the items description.
So a signal source, labelled as "outbreak", in an outbreak system, will contain materials from the chemical line, and higher grade signal sources will be more likely to contain Pharmaceutical Isolators.
As a final note, material traders are a good back up, but it's very frustrating to simply never find what you're looking for, and instead grind up six times as many materials that will spawn, just to trade them in. If you need a lot of say, Military Supercapacitors, which are usually used in weapons, which you usually use more than 1 of, it means you'll need maybe 20-30 of these, this would be 2-3 correct HGEs.
Or 12-18 incorrect ones.
And if you happen to need those "incorrect" materials for something else as well, then you need to visit even more HGEs, as well as frequent visits to traders to make sure you're not too full.