jefferywhat,
You bring up some good points.
I'd like to say though that the reason I like the question I came up with so much is because it brings together a number of important things that simply can't be done by pointing out flaws in their teachings.
1. You are challenging them to use the bible alone, something they that desperately want to do. They love the idea of opening up their Bible and proving something to you. By asking them to do the impossible, you are forcing them to see that their "Bible only" message is a myth. You are forcing them to admit that the Bible alone is not enough to prove their message.
2. You question a core idea taught by the Watchtower, mainly that their religion has been chosen by God. Usually JWs never want to defend this publicly, especially with people they do not know. You have brought some skeletons out of the closet and now they must look at them.
You can argue about many of the questionable details, but to me this question gets beyond things that could be labeled as "foolish debates" by the JW. You want to know if their religion was chosen by God or not. That's a pretty big issue, one that they cannot prove with the Bible alone. It puts them in quite an uncomfortable situation.