The best advice I can give you, if you want to go down that path is to asks questions and appear, for the very least, very interested in their thoughts. You can also make it personal. For instance,
How do you personally feel brother Elder about ... a taboo subject...
You would be surprised how many elders have a split personality disorder. They, like most people, have personal thoughts of their own that are not inline with the watchtower. However, when they are wearing their Elder hat, they suppress those away and answer anything as if they were watchtower articles themselves.
If you keep bringing them back to their personal views, such Elders will be conflicted, and most likely, at the end of some time, will saying something like: "it doesn't matter what I personally think." That is when you'll have them in your corner. You can than say:
"Then why does it matter what I think? If you are not free to express your personal conscience, then why would you seek out the details of mine. Like you, I would like to keep it private and like you, I believe I have the right to do so."