This isn't minecraft we can't enchant a pickaxe with Fortune III. Bleeding edge mining is not going to be a satisfactory excuse unless Eezo refinement techniques miss a huge % of the viable product.
Okay but this is Revy. Like, I get that there needs to be some sort of technological basis for "Things Be Better", but at the same time, Tony Stark Genius can also be described as being a Technology Flavored Wizard. We don't know the current state of eezo mining, so having Revy poke at that entire situation for a quarter should at minimum give us an understanding of what the "average" is, what the theoretical if super expensive "most efficient, effective, and advanced" option is, and depending on the state of things Revy may have time to do her technosorcery to it before even touching on actually going beyond existing methodologies.
Reviewing the Tech Tree and the Character Sheet, an Advanced Construction/Utility/Mining Drone that uses Biotics/Mass Effect Fields for material handling may or may not be more effective than current eezo mining methods, but it sure would be
fancy at least, and a useful testbed for other drone related technologies/uses.
Okay, so, a couple things.
First, I think you missed or skipped over the "space is big, go somewhere were people aren't to set things up" bit, or at least the implications I meant by that. I will revisit this in a moment though.
Second, Omega is a huge eezo mine/stockpile/whatever the hell it is responsible for the supply and sale of some ridiculous amount of the Terminus, implied to use truely atrocious mining methods with very limited safety measures to meet Aria's quotas. That's one source responsible for supplying significant percentages of the needs of a whole ass half a galaxy. If we limited ourselves to "one PI owned mine", we should almost certainly be fine in terms of "where is their eezo coming from???" measures.
Now, to get to the previous point.
Space is huge. Space is
tremendous in size. And existing FTL measures are honestly kind of crap.
My memory is a bit rusty, but I'm fairly sure that there are areas in ME 2 and ME 3 that you can essentially only reasonably get to due to getting fuel expansion upgrades, and that's with the Normandy being a top of the line experimental military ship meant to be as self sufficient as possible for both its original mission profile (stealth frigate) and its revised mandate (shuttle a Specter/Savior of the Galaxy around on the job).
With repulsar propulsion systems, Arc reactor power sources, and the multi-core ME drive systems, we have the ability to reach areas of space that are otherwise impractical and unprofitable to even attempt to reach, allowing us to set up infrastructure well outside normal operational parameters.
If we vet a particular group of staff, give them a bunch of VI and drones to help with labor, and use QEC comms, we can have PI infrastructure set up practically anywhere we want, while also being outside the normal easy view of galatic spy organizations.
From there, let's say we actually find a source of eezo large enough to set up a mining facility. We do that, tack on a "proprietary processing center" onto it, and use our "revolutionary developments" to cut in our artificial eezo alongside our "natural" eezo mining harvests, while also beginning to break into a new tech industry of eezo mining machinery if we have Revy spend a Quarter on the topic and then license out what she technowizards up.
And while we're there, out in space well beyond easy access to anyone, we can see about turning whatever system we're making use of into the most heavily fortified production center in the galaxy and somewhere that
should be sufficiently Reaper Proof to allow us a fall back option if things go to super shit, if we don't just turn said random solar system into our main base of production and research.
Though if we did do that, we'd likely want to actually have that Advanced Construction Drone with Built In Biotics as well as a Super Dreadnought Construction Ship to actually coordinate and process all of the materials needed to create enough powerful weapons to make a system Reaper Proof.
To return back to the original point though, if we make whatever cover story we do set up far enough away from easy access that people can't actually go in person to check things out without being Super Obvious, then it doesn't matter if we have an actual eezo mine or not to launder our artificial eezo through, we can just slap down sufficiently armed "no trespassing" signs that people get shot if they want to get close enough for proper answers.
We would probably want to work on an advanced "Astronomy" VI at some point though, to handle a lot of telescopes for surveillance/protection purposes, so we can see people trying to sneak around said "signs".