I hate to say it, but I think you're being a bit too focused, and that's making it a chore for you. Engineers can be rough if you fire up the game one day, decide to get DD5s and then work your way down the ingredient list, jumping through hoops for the stuff.
Instead, start keeping an eye out for HGE and other mats while you're about your business. Make keeping an eye out for materials part of your regular play, then it will not need to become such a time sink. You'll have still spent the time, but it won't have been all at once, when you didn't want to do it.
That was my original approach. I gathered up everything I could for about eighteen months, then decided to fully engineer my mission runner. My year and a half's worth of materials didn't last me through my first engineer. I probably should have been more careful what I traded at the materials trader, but that only shows just how broken the 'solution' to random material gathering is... ☹
It's Gambler's Fallacy to think that RNG not throwing up something for a while means that it 'should' soon. That's not how random works. Dice have no memory. Grinding your teeth and getting frustrated at 'RNG' because something 'should' pop is just going to give you ulcers, because your head is telling you something which is not mathematically true.
Personally, I put myself in the position to bump into things when I am about my business - check the system state and favour 'working' in systems that are likely to spawn unusual stuff or stuff that you do not have much of, then keep an eye out for it in the course of play - en route to CZ/Rez, for example. That way you maximise your chances of finding it - by being in a system in the correct state - without having to invest any effort over normal play, other than pointing the nose at USSs, to see if they are 'good', and popping in if they are.
If you're in a large ship, always carry a collector controller, and pop a limpet after each combat [except in CZs, obv...]
Oh and mission rewards. Money is pretty meaningless after a while, so I'll always plum for high grade mats that I might need later on, rather than just the cash.
See above. Mileage varies, but just picking up stuff as you go along didn't work for me, I suspect I'm not alone in that.
Wolf 497 ? Needed some last night, was expecting a couple of hours of slog to get them. Decided to make a very slow 57ls crawl to Buffett Vista to try and spawn high grade emission USS'es, got one about halfway & lo/behold, 4x improvised components. Like another poster on the first page, I consider this payback for all the times I have had to fly around for hours trying to find crap like this.
I knew reading this thread was going to be a mistake... So now we have to hit the hazard lights and slow to a crawl to get the damn things to spawn?

I don't know about anyone else, but I'm sick to the back teeth with the ridiculous number of things we have to do to get mats to even appear. It's beyond frustrating. Has RSI infiltrated a professional troll into FDs office? Why is it so bloody contrived to get the coins needed to buy upgrades? There might be a worse crafting system out there, but I wouldn't play it, so why in the name of all that's Holy do Frontier think I want to play their stupid grind just to get my ship halfway competitive?
They are also common rewards for Passenger Missions.
Yeah, of course they are. Because tourists would be bound to have half a dozen engineering materials rolling around their Samsonite bags, next to the flip flops and duty frees...
If anyone from Frontier is reading this, consider the following: I gave up on Elite last month. It was my childhood dream, it was fantastic to see it realised and I had close to five great years playing it. But power creep makes engineering mandatory, my fleet (five year's work!

) is obsolete and the engineering process is such an enormous pain in the arris I just can't be bothered flashing the game up.
If you see long time players leaving, maybe you might want to take a look at why they're going. Turning away loyal customers in droves, making the people most invested in your game, those most likely to pay for future content, look elsewhere for their entertainment, really isn't good for business.
I haven't uninstalled.
At this point I'm in denial, telling myself I'll be playing again soon, but I've got shelves full of games that I thought I'd get around to playing again. Right now I'm back to flying sims. Study level models are insanely difficult to learn to fly, much less hold your own in PvP matches, but they're also immensely rewarding to get right. There's no RNG to contend with in a sim, either your skill and luck hold or you crash. That has long term appeal, an incentive to do better each flight. It beats nine Hells out of hoping that the random number generator will be kind next time around...