Nice post Masterstroke, well laid out and fun to read. Sounds like you had a good night mate.
Sounds like your game with Kate was pretty solid man: use of your own openers and routines, false time constraint, DHV with an amusing routine (you might have to elaborate on that white watch routine mate - it was epic and I might steal it lol

), and you showed that you weren't intimidated by her by being the one to hand out the cool points to her. All in all, nice work. Congrats man.
Now for the sticking points. A bitchy friend is really annoying if you can't win her over, and can easily block the way to more satisfying closes (kcloses and fcloses) if she's really bad. No matter what though, you should still be able to get the #close if your rapport with the target is strong enough, and I think you probably should have gone for that before Kate got dragged away.
Asking for her number is, obviously, a pretty huge IOI on your part, so you have to be careful with when you do it. If she's about to be dragged off for reasons other than disinterest, it's best to just go for it then, in case you don't see her again and you lose her. This isn't ideal though. In my (limited) experience, I think the best time to ask for her number is in the middle of a conversation that is genuinely interesting. If she has just given you a pretty big IOI, reward her with your huge #close IOI, saying that you guys have so much to talk about, and in case you don't finish tonight, you'd like to know you can meet again sometime. If you do this with confidence, and then go back to what you were doing before when she's done, I think this generally feels pretty natural. Another small point is that a command sometimes bypasses the social conditioning that makes her freeze when someone simply asks for her number. What I do is hand her my phone with 'new contact' selected, and say "Here, stick your details in there so we can continue this another time." or something to that effect. That works well if she's just made you laugh a lot actually.
As for disarming the obstacle, I find it's often helpful to run game on her as well. If she understands her friend's admiration of you, she will be less likely to stop you isolating her later, unless she is a jealous bitch. Run routines on her, and DHV as much as possible. Another bonus is that your target will see you being confident and outgoing with another girl as well as her, showing that you are well socially adjusted and that you have options. This might create jealousy in your target as well, which is probably a good thing. The other night (field report pending), I left the target for a few mins and isolated the obstacle. I made her laugh, and then whispered in her ear that I thought the target was cute, and asked if she was single. The obstacle replied that I was 'in there', and that she was going to leave the two of us alone. lol. This won't work on every obstacle though, so I was lucky. An alternative that might work (untested, though) would be to compliment the bitch on her bitchiness (fire, fiestiness etc.), thus disarming the bitch shield? I would be curious to know if anyone has tried this successfully.
Anyway, hope that helps mate. Well done again Masterstroke, and here's to many successful sarges in the future!
-Darkfield.