I just got an exquisite focus crystal the other day - first one. Just had to do a simple trading mission. Didn't have to be allied or anything.

My advice with engineers is have fun with it. Go for easier obtainable things and while you are getting those you will stumble upon better mats. For example I wanted the lvl 5 power plant so bad but I had a ton of mats for my lvl 4 missile modifications. All I needed was tin. So I went out to get tin - spent a good 3 hours doing it. Got enough stuff to get good rolls on all 4 of my missile racks. It was satisfying and was doable in one gaming sessions, something we all want.

When I was done doing the missile racks - I go to recheck the mats needed for the lvl 5 power plant and boom I realized I picked up quantity 3 of tellurium while I was getting Tin.

I guess the point is instead of hunting so bad for a specific modification when you have none of the items. Work towards modifications that are easier to obtain (levels 1-3). You will get the satisfaction of improving your ship, you will upgrade the engineer and you will stumble upon higher lvl mats for the lvl 5 stuff and realize you don't really have to grind for them. You just have them from working on your ship.