One thing I neglected to mention was that I was able to use Iridar's ADVENT Pistol for primary when dual wielding, but I removed that mod a while ago due to the fact that he doesn't allow the pistol to be upgraded (and has no intent to change that). Just trying to come up with a solution while using only the pistol from ADVENT Armoury.

So... When the next mission came up, my gunslinger managed to scrounge up a primary version of the pistol. Somehow. It's weird, but it just wasn't present when I was trying to change her loadout outside of mission prep. That's XCOM, I guess.

https://steamcommunity.com/sharedfiles/filedetails/?id=1571006350