I understand the "real life" thing in theory. A gun can kill in one shot. But so can any of the weapons on the equipment list if it hits the right spot on the target. That is one of the issues with turning real life into a game. A lot of people have tried to make guns work as RPG weapons, and I don't think anyone has really been able to do it outside of a story game that doesn't use HP but allows for narrative, but I haven't played or read every game in existence, so I won't claim it's impossible.
I mean...a sword or ax can take a limb, but that isn't put in the rules. I feel like the designers didn't put rules in for chopping off the arms of a warlord, making him unable to use his battle ax, thus removing him from the fight on the first turn because it sort of ruins the game play. Dragons have 300+ hit points so the Paladin can't take it's head and end the battle before the rogue or the wizard has a chance to act. Guns...or early guns like the ones being discussed here were highly inaccurate. That isn't reflected in your rules either.
Plus, you gave the class Sneak Attack. Doesn't that make their damage output high enough?
You mention in point c) that "they don't add ability modifiers until later". I don't see that mentioned. All weapons in 5e get ability modifier added to damage. Why not your guns? That is a change to the rules that I don't think is necessary. I get the idea that upping the damage but removing the ability modifier randomizes the damage output that might feel more like a 'real-world' gun where a bullet might be a flesh wound or a fatal hit, but it changes to many of the base rules that all the other non-gunner players are using. If you roll back the damage dials it still works. I think. This change might work in a different game where the rules are already set at that level.
In the end, I am not trying to be overly critical. You made an interesting class that could be fun to play. I think that one change is needed, but I could be wrong. I just feel chasing "real-world" results in a fantasy RPG...well it doesn't work. But that is just my opinion.
I don;t feel you were coming off as defensive or a jerk. You have your opinion on how this could work and mine is different. That's all.