I've come to the conclusion that everything is so broken or RNGed so I'd better stick to what's working. Even systems that usually have HGEs, don't always have them for hours, maybe there is a cool-down period or something.
So I made myself a circuit around Achenar, made of highly populated Imperial systems and a material trader nearby (Lombi) and I started collecting Imperial Shielding: collect until 100, then trade 90 for 15 others, then go back. I can even do a 40 minutes HGE twice if I move fast. It's boring, but it works. No more searching for states and factions. Yesterday evening, I found ONLY Imperial Shielding, no matter the faction state.
I think in 5-6 days (I can't play more than 1-2h per evening), I'll maximize all of my Grade 5 (currently from 25 to 70 each) and then I'll go back to engineering my ships (after maybe a new excursion to The Bug Killer and Jameson's Cobra). I just want to be able to do any mod without thinking about materials for a while... if possible, because you cannot do more than 7-8 lightweight mods that requires PRAs for example, without empty your reserves for both PRAs and PLAs. Same with others.