That's interesting, I'm a heavy FPS gamer myself so I did wonder if that FPS/dungeon crawler crossover might be jarring for some people, but I thought it would be a challenge to make it anyway. Would you say a game like Legends of Grimrock is also just a clunky FPS? That's also real time, and was one of my inspirations for how I made this.
Yes the spread mechanic does technically apply to the AI (sometimes you can see them hit the wall or ceiling beside you). But as you noticed they only fire in bursts, so it's in a pretty limited way.
To avoid getting hit so much, the best approach is to be further away from them. They're not as accurate as the player is (especially if you control your bursts well). You can also anticipate their moves and be ready to shoot as soon as they come into line or as soon as they come through a doorway. The shotgun on the second floor also lets you shoot them in groups and very easily hit them before they get in line to shoot you (obviously only use this at close range though, it's weak at long range).
The enemies would have been more dangerous if I'd had more time XD I haven't added any hearing mechanic to them, so you can shoot right beside them and as long as you don't shoot directly at them they wont notice. There's also some room for improvement for where they choose to move. I wouldn't have made the 2nd floor encounters so big if I'd had time to make the AI smarter.