I know this is an approach that some guys will turn away from, but personally I go to a party with one thing in mind - to have a good time and meet new people. If you go with expectations of meeting or getting with women, you will look desperate, or at the very least you will look a little lost.
Talk to all the guys. Talk to the girls. Talk to their friends. Make drinks. Be interested and interesting, and then as a natural result of doing this over time, women will respond. Next time you go to a party with a similar group, you walk in, people recognize you, next minute you're being introduced to some girl who may or may not think you're cute - but at the very least, if you are displaying high social value (ie the other people at the party gravitate toward you on entry to the party) then you will be raised even further.
This is my approach and it has worked wonders for me. I no longer go to parties thinking about meeting girls. But it happens naturally as a result of my eagerness to expand my social circle. Just something to think about...
By the way there is absolutely truth to what has been said about girls who will pick out a guy they find cute straight away and persue him over the night if they have the guts. Being a generally social interesting person just helps make those encounters more likely. It also helps generate just that little extra bit of interest to help swing them one way or another.
"K thanks for your time ladies" no no no. Are you a salesman? Are you a Jehovas witness? Why are you thanking people for their time? Women at parties? Are they thanking you for your time? No. So why in the hell would you say this?
Look, the problem so much of the time with guys who can't meet women at parties provided they have sussed their dress, look, hair, etc etc is just down to the fact that there is much work to be done on their personalities. You can't fake being interesting. You work at it. You learn, read, watch, pay attention to everything around you and you meet more people, you chip away at yourself like a craft, and you can get there. But if you're running out of 'things to say' you're doing it all wrong. There are no 'things to say'. There is just being somebody who's interesting. If you can't captivate a group or a person in a non threatning, non cheesy, non 'pickup' way, then you have work to do, like all of us. Keep working. Just don't look for the immediate fix - look for the root of the problem.
The mysterious cool guy look? Sure it works if you're really attractive or if you're totally her type. But if you're just a DUDE, just a guy at the party with nothing on the surface that screams "OMG TAKE ME NOW", then you have to be more engaging, period. My success from parties is due to the fact that I walk in, say hi to the host, be friendly, be funny (but not silly), be entertaining - I challenge the girls, I don't suck up to them - the last girl was having a chat to her friend about some guy, so I just jumped in casually and before you know it I was reading her texts, making them laugh as I pointed out how badly she was being gamed by some poor sucker, watched as another guy tried to circle around her, just basically being somebody who is fun and doesn't have any immediate aims to bang her. Meanwhile I'm still meeting new people around her and talking to my own friends, so it's not like she has my 100% attention. She's just a girl at a party, and I'm meeting lots of people. And this is why women warm up to you - because you're NOT that guy who's circling, you're not that guy who seems like he's playing a game, you're not the guy who comes in and says stupid **** and calls them 'ladies'. Now - on the surface this looks like my big 'game'. And there was a time when I'd read stuff like this and be like "Wow, I gotta try that". But you know what, if you're 'trying it', if you're faking it, if you're doing it as a big move, you're probably going to fail, hence why most wannabe PUA's look like out of water fish when they try and pickup girls. This is the result of me spending several years chipping away at every aspect of myself and finally coming to terms with who I am and letting myself relax, losing my false expectations and getting all the silly PUA stuff out of my system.
Obviously this approach is not for everybody, you have to find your angle and run with it. I'm just saying you need to rethink the whole concept....stop thinking about 'approaching'. Don't think about trying to think of things to say. That's just putting a plaster on a deep scar. You need to get deeper, think more long term. This is not an easy fix, but it's something you have complete control over - you have time to think it through.
Finally I'd suggest getting out of any stupid 'singles' parties. Go to regular parties. All the stuff with icebreakers etc etc as you describe just puts pressure on you to find something that may not be who you are. You need to find your element, your place of peace. You can pickup women with your friends around if that's what it takes to keep you in the vibe where you are the one in control.