When I have been in similar situations, I talked to the folks who were on my side and said, "Hey, I need to use the room to try to get with her. Can I have the room from this time to that time?" and then if there were any other people who I couldn't do that with I just made it a point to find out their schedules and pick a time they'd all be out.
The thing with getting her away from the friend -- you need to tell her you want to do something just the two of you. You can frame it as "I've really had a lot of fun with all this group stuff but I kinda hoped to do something that was just us two. Would that be cool?" If she agrees to it, you are basically in.
Biggest problem sounds like you're not actually at the point yet where you can just pull her to the room -- it's still in the "tentative flirtation" stage. I would just make the focus on finding a way to get around her physically, so you can use ample touch, whether the gay guy is there or not. If she's into it, once he figures out what is going on he should give her her space. Gay guys are huge sluts themselves... he's not going to cockblock her from getting some vacation dick. If she's feeling you, you can sort logistics then.
If logistics are screwed, you just get a lot of touch going, get her turned on, then tell her, "I really want to be alone with you. Where can we go?" and see if she has ideas, and if she doesn't, but she agrees, at least you have buy-in -- but you will need to figure it out fast. You might want to reserve a little extra cash to book an impromptu room a love hotel if nothing else manifests:
Romance in the air? Love hotels are a discreet place to meet.
I think you're totally right about tentative flirtation. It went really horrendously bad. Possibly going to be hilarious one day, but I was in no mood to enjoy it then.
Following is a FR:
Context: I had a really bad day where I had a tense negotiation with a good friend and we both lost a lot of money. Have work stress too so my state was abysmal.
End up making plans with her for all of us to meet up at a bar. I enter and my state is just plummeting, I'm massively in my head. End up getting shit tested a bunch by everyone there (including my brother -- what a dick move) to the point where it's like a humiliation orgy at this point. I decide to take a walk with them to see this chruch at night. I do flirt a bit with her on this trip, we pull ahead of the gay guy and my brother and chat a bit, but like nothing sustained. I can't really do any kino or anything because she pulls away, or maybe she's waiting for me to just cave man her or something but that's not in my personality to do that. For context, this gay dude is autistic as fuck and not the open minded have fun whatever type. So I think he would judge the fuck out of her for being a slut. I also think he doesn't think I'm good enough or something.
So anyways, we walk back, and she is clearly trying to show off, walking in front of me, dressing slutty, etc. But I can't make a move because everyone is there and I just feel reactive. She keeps isolating herself in ways that I feel are approach invitations and we keep exchanging glasses.
Eventually she goes up at night to grab a glass of water. I figure well this is it if it's ever going to happen. I start trying to chat her up with bullshit contextual teases like nice water or something. The point is this is not tight game. But anyways, I end up saying at some point I think she's cute, and she hits me with "I have a boyfriend." I realize at this point that I am basically starting back at square one in terms of opening. So I basically say some standard thing like, oh cool I never asked. Is he single? She laughs, and I continue the conversation for like 30 seconds longer and she says she's going to bed. I'm just left standing there in front of the sink sipping my water and being like, what the fuck just happened.
If I could replay it, I'd have been approaching more throughout the day to keep my state decent and congruent with who I am. Then, that night in that interaction, I'd close the distance between us (She was at the sink, I was about 6 feet away, leaning on the counter angled away from her to not look needy), and say something like I can't decide if I like you or not (kind of true lol). I wouldn't have given away value by saying she's cute. I misjudged that at that point, she had concerns about value and congruence. Then I would have "venue changed" as in just led her outside the apartment to chat and rapport for a bit.
AND, I think there were chances to salvage the set even after the boyfriend/I'm leaving bit. I could have chased her down and spiked emotion then pulled back -- though then it becomes a low probability think. The reason I say this is she seemed to not want to leave things on those terms "right.. I forgot you don't have instagram... well... thanks for hanging out" Like she was probably trying to put me in the orbiter zone, but if a girl is talkign to you, there is something she wants, and there's a chance.
Anyways, the bigger picture is that the feelings that put me in after the "rejection" (baad) showed I wasn't in a place of abundance. Which is tricky because I have more important things than girls to focus on right now in terms of career, etc. for the short term. But I am still a virgin at 25 which means I really need to fuck and will of course be tempted to drop anything when an opportunity presents itself.