When sticking to dates, if he attempts to go on with the presentation on how they came to 1914, would this be the time to mention 586/587, or wait a week and 'do some research?'
As soon as he mentions 607, disagree with him. Use Wikipedia if neccessary. Gently coerce him into agreeing to find an independent source that agrees with it.
You don't need to know Allymom's KISS aproach to use it. You should be able to get him to do it for you. You need to try to get him to give you a list of kings from Nebuchadnezzar to Nabonidus, showing what years each king reigned in. What he gives you should match Wikipedia. If it doesn't, ask him where the mistake is? If it does match, he has just flushed 1914 down your toilet.
His best option will be to divert your attention, by showing you all the reasons why he thinks Neb's reign begins in 625 instead of 605. Don't fall for it. All of his reasoning is irrelevent if his answer is contradicted by history, which it is. Make sure he gets that point. Restate your request for a correct list of kings from Nebuchadnezzar to Nabonidus, showing the dates of the reigns.
I think he can get all of the info he needs to do this from the Jan 1, 1965 Watchtower, but you might want to pretend you don't know that unless you have one.
You must control the direction of the conversation at all times. They are masters of redirection. For example, rather than discuss the item/scripture you brought up, they will show you something that they feel contradicts it, and hope you forget your item/scripture. Nip it in the bud, and get them back on your 'proof'.
If he says he will get back to you next week about that, and wants to discuss another subject with you now, it's time to go fishing/whatever and you're in a hurry.
Cheers
Chris