How do you rule insight checks during dialogues?

I'm running a game with a very active player that loves getting to the bottom of things.

This often poses the problem with dialogues and Insight checks.
If there are NPCs he (sometimes justifingly) has doubts about, he goes "INSIGHT" after almost every new statement as if he's the medieval fantasy version of Phoenix Wright.

I tried several solutions so far and none of them make me particularly happy:

• Contested Roll (Insight vs. Deception) after every callout
  -> dumb, because it's numbers game where he sooner or later "wins". Not to mention it makes the check feel like a binary lie detector instead of a gradiant line of sensing someone's motive.
• After his first callout and check: give him additional information during the conversation based on his roll.
  -> feels like I'm taking his agency away and serve too much infos on a silver platter
• When calling an Insight check, he needs to describe what intention he wants to gauge. For example as an Insight check for the phrase "We meet as at midnight at the docks" he asks as check-question: "Does he want to meet us there because he thinks it's a good ambush location for his cronies?"
  -> feels for me more like an Investigation-check since it's based more on logical deduction than sensing a motive.

In the end it feels like a thing that has no elegant solution. It's also no major problem since me and the player are very understanding with each other but I'd still love to provide a system that makes us both happy.

So, what's your way to do it?