MJ: Or I could try and play "stump the chump" with my wife present, which carries its own risks and possible alienation of the wife.
I recommend this approach, but not with this objective. Stumping the chump is argumentative and will likely result in alienating your wife. Calm, reflective, logical inquisitiveness and respectful reminders of questions unanswered will do the job nicely and not alienate your wife.
In other words, hear the fellow out. Ask questions you know he can't answer, no matter how scientific he is, like "Why do Jehovah's Witnesses tie Luke 12:32 to John 10:16? Couldn't the other sheep be referring to the Gentiles?"
It isn't a scientific question. It is a theological question. And every JW is theologicless when it comes to answering it, all the way up to and including Ted effing Jarasczssczzzczs (or however he spells his name). It is obvious from the timing of the statement and Jesus anticipation of where things would go that he was referring to the Gentiles. Likewise, the context of Luke 12:32 makes clear that he was not comparing the little flock to a larger flock of sheep, he was comparing the little flock to the rest of the world, the "nations of the world" according to the NWT.
There are many more similar ones we could put you onto. Questioning theology doesn't require a lot of smarts, and you can point up how he evades answering in a joking way while maintaining a respectful camaraderie. Your wife will be amazed how many things there is no direct Scriptural explanation for.
The brother will likely say something along the lines of, "Well, that's pretty deep stuff. It would probably be better if we laid a groundwork first and then worked our way up to that." You could respond, "So, your saying there is a crystal clear Scriptural basis for that?" He will definitely say, "Yes." You could respond, "Well, why don't you just show it to me, whether I understand it or not. I'm sure my wife will understand what you show us. She wasn't able to answer when I asked her. That's why she invited you over here, to answer the questions she couldn't."
You will get more hedging and you will notice pronounced squirming and stalling. Then you will see a light go off. Prepare to be evaded again. Just politely ask, shortly into the different path of inquiry, "Now this does relate directly to why Luke 12:32 and John 10:16 are linked together, right? Because, I'm not seeing the connection at all." Look to your wife, "Do you understand how this ties into my question?"
Talk about calmly putting the screws to the poor chap!
Respectfully,
OldSoul