How to drive this forward?

From my perspective, this is too platonic. You seem interested in her, but you're just hammering questions that are mostly logical in nature. I would go the "what do you do for fun" route, which I get is a continuation of the criticism Im giving, but I think it will set up opportunities to tease and begin using the "we" frame. Start adding in questions that evoke emotion, talk about yourselves as a team, add humor. I think sexualizing or going for a soft close at this point is too out of left field. Begin to reframe the platonic context that exists here

"we'll have to add one more item to the agenda"

definitely sexualize and add humor/playfulness to the convo