First of all, thanks for the review!
I just got my First Curse, and took it for a brief spin. I've only used it in a single strike, so it's too early for me to be sure one way or the other... But my first impression is that I don't like it at all.
My problem with it boils down to this: its archetype and exotic perks run completely counter to each other.
In order to trigger the First Curse's exotic perk, you need to score a precision kill. But the gun itself has such poor range, accuracy, and aim-assist that scoring precision hits is a lot tougher than it is with many other hand cannons. I should mention that I've only used this gun against Vex so far, and they're not the easiest enemies to score precision kills, but I used to 1-shot vex goblins all day long with Fatebringer, even after the 2.0 update.
As you said, the gun's real stand-out feature is the impact. This makes it a great choice for tackling tougher foes like Minotars, Captains, etc. but again, these targets are not good fodder for the gun's exotic perk. As powerful as it is, you'll still need most of your clip to bring down high-level foes. Even if you do manage to score a precision kill, it only lasts until your next reload, which is never far off with a gun like this.
All of this makes me feel like the Forst Curse is better suited to tackling low level mobs, where you can score precision kills more consistently. The thing is, the high impact is wasted against such targets (you can 1-shot kill enemies with weapons that have far lower impact). Again, the slow rate of fire and poor range/accuracy come into play. I'd much rather use my Dead Orbit scout rifle; far easier to hit headshots, even while hip firing. Enough impact to 1-shot level 40 tier 1 enemies, fires so quickly that I can still trigger Tripple Tap even if I miss a few shots between precision hits, and it has Firefly so everything is exploding all the time :D
Again, I want to spend more time with First Curse, but my early impression is that I can't think of a situation where it would be a weapon I'd want to use... especially at the cost of an Exotic.