Thanks to some good people on this board, I'm pretty sure my next run of "Arms Dealing" will clear the quest.
What REALLY irks me though is that the timed quests in this game seem impossible without some form of "cheating," IE pre-killing enemies and/or leaving a car in a good spot to teleport too.
If the quest description gave you a heads up on this, that would be one thing, but in my mind, any quest that is essentially unbeatable the first time you get it (that is, needing prior knowledge of it to stand a chance of beating it,) is poorly designed, nothing better. --- Funny how GameFaqs tags the word "faqs" as mispelled.
I didn't really like the timed quests, even after I realized I could use the catch-a-ride stations to teleport and make them easy. If they wanted to include a feature with a time limit, I would have preferred if each area had a vehicle time trial course. Then multiple players wouldn't change the difficulty of the mission, you couldn't use teleportation to make it easier, and Ellie's relic might be useful for something.