Some things I use all the time when a conversation gets interview-y:
Girl makes some claim. Doesn't matter what, as long as it's some claim, about something. It's better if it's something she's kinda proud of. Or better yet, if she likes something that you hate. Or if she has something that you don't have.
Then I go: "Alright. That's it.... I'm outta here!" Then I start pivoting like I'm about to just leave.
It's a joke. I don't actually intend to move. You did it right when this gets her laughing. Then go: "Nawh, just kidding, gimme a hug." Then hug.
This creates contrast. It's a kind of push and pull I suppose. You did some push pull but it can improve.
You can also very gently push her away, then pull her in, physically.
Experiment with saying stuff like "OMG no way, I love that!" While doing opposite body language. Like gently push her away. But then you go - while smiling - "Omg I HATE you!" But give her a hug.
These are verbal things. You probably got flustered and went into interview mode. Happens to the best. But that's when it's good to really stop and go "Hey... Snap out of it. This is where you gotta EXPRESS yourself. And be comfortable expressing yourself too!" In a fun and light-hearted way. Like, it's hard to explain, but if you know how to let lose and just say something weird off the top of your head. Helps if you went to improv classes, but it's not a requirement.
Second. Stop asking her questions.
No questions allowed!
You can now ONLY make observations or make claims. That's it.
It's a good exercise to do when the conversation get's too interview-y.
You wanna ask where she bought her green dress. You wanna ask why she likes green. STOP IT! Instead, take a GUESS, and make an assumption. "Hey, I bet you bought that dress at Disneyland!" She'll go yes or no (in this case most likely no). Then tease her for it: "Total Disneyland dress!" Not to be vile or evil. Do it with a smirk. If she gets angry, say you're sorry and change the topic.
Her dress is green. Again, improv land. You can do a set-up. A set-up is when you ask her a kind of leading question, without an obvious conclusion. "Hey, wanna know what it means when people like green?" It's kind of a rhetorical question, because the only good answers are "What?" or "Yes?" Then make something up: "People who buy green stuff are most likely Irish, according to statistics." (Horribly bad joke, but maybe she'll smile...) (Ok, don't use this joke...) The point is: It'll have her "participate" a bit more in the conversation. Then you can use it as a tool to add on more claims, more observations, and so encourage her to contribute even more until you have a flow-y exchange instead of an interview-y one.
From then on, remember to bump her hip at some point. I rewarding her for saying stuff I like, such as: "Omg, from now on you're my wife!" Then lead her down the street. But whenever there's a lamp post lead her directly towards it. Don't bump her into it, but lead her until she goes "Hey wtf!" or until you notice that "God this bitch must be blind, but I don't wanna hurt her" so you abort like one millimetre in front of the thing by going "Hey watch out!" Then always blame her for what you did for extra bonus points. With a smirk. It's never serious. You want her to hit your shoulder in a friendly way.
Keep getting incidental touch, or lead her by the small of her back. Or - when crossing the road - take her hand and lead her like a little girl. She'll love it. Bonus: You're now holding hands like gf/bf. In a super smooth way. (Or she'll not want to hold hands, and... well... Probably cut the date short.)
At some point you should stop being all goofy. Do this when it gets emotional. When you feel it. And you're close. That's when you go for the kiss. And not out of the blue.
Anyway, just some ideas off the top of my head.