Interesting case you have here, I have been with a lot of women with boyfriends.. Not intentionally most of the time, but I never see it as a problem if she seems down. Even married/engaged women is sometimes DTF, so I would probably test it out! But I would set a limit to two dates, if there's no fuck by then.. drop her! It's just gonna drag you down by then. I don't see a problem with coffee dates at all, sometimes it even escalates to some drinks later! But as Big Daddy says, you get a much more intimate conversation, much easier to deepdive if you ask me. Yesterday I scheduled a coffee date, ended up with a beer down at the harbor. Really weird actually, we saw a junkie shoot heroin and then he went on to fish! hahah wth.. I always like it when it's quiet, if you're both comfortable, then it's easier to have her open up. This girl I was with even told me: "Wow, I have really told you so much about myself that only my best friend knows about me." Tossed in some Chase-frames and even asked about her toys in her night drawer -> went to her place and you know the rest of the story. So quiet places work best for me
And as mentioned before, I don't see the time set for the date have to put any stoppers for you. If you of course actually can make it at that time. As for paying for the coffee, since she's in a relationship I wouldn't pay for it. If she was single, I don't see it as a problem because it's what? 3.50$?(From Europe, so don't know your prices). I rarely pay, but sometimes I just do it as of convenience. So I think it's up to you on that point, some guys always pay for her coffee, and it doesn't really change anything.
Hope she text back and is DTF, as girls that are committed can be really fun. (Fuck at weird places and what not, do weird shit that her boyfriend doesn't want to do with her or for whatever reason). And when you have fucked her.. You have ALL the power, if you want to end it, she can't do shit!

And you don't need to put out the "I don't want a relationship" and all that shit, as it's already worked out because she has a boyfriend.
Cheers
-TC