Here's an idea. If everyone wants to see a copy of the 1991 form the Society filled out when subscribing to join the UN to see if it is consistent with their claims (which can be viewed here http://www.jehovahsjudgment.co.uk/watchtower-un-ngo/) then instead of beating your heads against a brick wall trying to get it out of the Society why not approach the UN itself and see if they have any copies of the form from that time? Better yet there must be other organizations that joined in that year both before and after the WTS, maybe one of them could be persuaded to produce a copy of their form.
That way if the form disagrees with what the Society and it's supporters are claiming then you have them dead to rights and this whole debate suddenly move to a much higher and more dangereous level for them.
There must be a lawyer somewhere who works for a respectable firm. a businessman who works for a respectable company, someone who actually works for an NGO etc that was DF'd at one point (or maybe not) that wouldn't mind taking such a bold step to get to the truth in this matter.
I would do it but I'm a nobody and no organization is going to respond seriously to such a request from someone like me.