What a dilemma! When both perspectives are useful, but they're initially getting in the way of each other.
Are there any 10,000 foot questions you can get them talking about? I couldn't find a good blog post for that term, but it basically means an overview from such a place where the details aren't visible, but the needs/goals are still there.
From personal experience, I attended a parenting class many, many, many moons ago and they asked us what we wanted for our children. Most of us wanted things like for them to be happy and fulfilled in their lives. That's the 10,000 foot view. The rest, like being a Nobel Prize winner comes later.
My best guess is that they both want the same end goal, but they're entrenched in their way of looking at things.
That's not a very concrete thing, like your card sorting exercise. I hope it's useful though.