Hey mate,
Something is dodgy with this lady here.
Before anything, I believe you're overthinking the whole process. I know you care but if you " pull " and cut off easily you know that your doctrine works. if you start to fell in ths spiral when you care too much you will eventually become what you guys seems to call needy. I know how you feel though because I have been there too and whenever I started caring too much things went batshit bad at some point. until one day I understood that let the things flow naturally is the way.
Coming to it now.
1) she got a dude but she hooks up with you and seems to flirt openly. bear in mind that if you acquire a lady that was originally with a BF chance are the day your relation is having a slow day if a knob with chat comes in like you did he might have a go on your gf's legs the same way you did.
2) now if you want to hook up things are pretty simple I think. I believe you're pretty much doing it right, but I'd say just do not think of the dude, it's not because Real madrid has a goal keeper that Barcelona never score on them you know what I mean ?
3) you're not offensive enough. You told her you could be friends, what the fuck mate ? you're not here for the friendship, I'd advice you take actions and invite her for a drink soon enough. you live not far from a beach ( or any nice scenery place ? ) get a bottle of wine ( red ) + two glasses hide em in your bag, bring her sometimes in the evening to the place when it;s quite and pretty and pull out your stash she will be stunned, you might as well do her on the spot.
4) if really she has a dude she will tell you. Birds try to give themselves good conscious by saying " oh by the way I got a dude " when things got heated up. our society always shame sluts so that's what they come with this way they can be like " I tried I told him I was a taken deal ". So talks her through and annhilates her boyfriends.
I'm going to give you a personal exemple. Decemenber 2015 I met a girl from NY she was trying to tell me how great her bf is but she was an advertising worker while he was a finance worker corporate to the max. So I told her " look, there is something shifty here, I hate to say that but you're very chilled out and have this kind of bohemians mindsetwhile he sounds like the archetype of the Finance prepi guy, arent you with him because you're closing to your 30s and you think it's time to settle down " needless to say I was knee deep 30min later.
so find out what's wrong, what the dude is if really there is one and eject him
Good luck, by the way we're going straight to hell because stealing someone's girl is a sin