Double Shotgun is pretty good, honestly.
Not really on that build, though.
The huge reload time is the issue; Two full seconds means that an assault shotgun, which can go six shots without reloading and has a nice 1.0 reload time, is better for that build. Give it a try, and remember that you're getting off two or three shots for every one the Double Shotgun does when you're judging it; I think you'll be surprised how often it's more effective, when you consider that.
The times Double Shotgun really shines are early on(when it does the most damage of anything you're likely to see, barring a very ammo restrictive early Plasma Rifle(UV/N!) or Rocket Launcher, when you have Shottyman(So you can reload it faster than its huge reload time by moving), and when you have Juggler(Swap to it, fire a blast, swap back to your main weapon and reload the Double after combat. It has enough kick to be really good in some situations this way.).
Edit: Oh, and Nanoshrapnel modded ones. But that should go without saying.
Huh... her damage is just that low then? That's not so bad... Might even give it a try on HMP, assuming I can ever get down there...
Heavily subject to protection, mostly. Lots and lots of little hits.
The usual threat is that you screw up, have your armor degrade, and suddenly she rips you in half in two shots. Shielded Armor's infinite durability is why things went decently there, not its resistances. I was rather surprised at how well a Blue Armor holds up against Mastermind, recently, before it starts getting damaged.
Never really tried SoB - is it really strong enough to compete with Intuition or Hell Runner early?
Pretty much build dependent, in my opinion. SoB is a massive boost to rapid fire builds, though, and you were using a Double Shotgun and a Plasma Rifle, both of which multihit. It would have been more useful than Finesse on that build for very sure, and I would take it over Dodgemaster in that particular case(Hellrunner 2 gives you a very adequate dodge rate for the most part, and you're not having to fight Cyberdemon or UV/N! accuracy bonuses.) as well.
Intuition vs any other skill is basically subjective, though. Some people seem to swear by it, I personally never use it, but I'm not big on informational skills at the cost of combat potential in any Roguelike, even when they are good enough to justify it(As I feel Intuition is.). Dunno why.