Yes, it's possible, and yes, BSG have of course thought about this. I have 0.83 rep with EOD, which would be 0.63 rep if I had a standard account.
These are arguably some of the most difficult quests in the entire game
Killing two flashed PMCs are among the easiest quests in the game due to the KS23 existing
I've gotten 7 labs keycards from 15 scav raids (spawned in my scav inventory) so if you just scavved and kept up your karma this can be done in less than a day
Tarkov Killer part 8 is incredibly hard, yes... but also only gives 0.02 rep
I'd argue that the boss killing quests are also among the easiest to do, and you get 0.1 rep without even having to kill gluhar. these have the same weight as tarkov killer part 8, so take your pick between that or killing reshala once
Unfortunately this just sounds like a skill issue.