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If the ip has been changed to the new server and the soa has been increased, you should just have to wait.
Last I did this, I believe it took about 8-10 hours for all of google's bots to be hitting the new server. I switched servers mid crawl.
Hope this helps,
One guess would be to block Googlebot and the other robots on the old site via robots.txt.
DNS updates take a bit of time to filter throughout the internet. I would leave it in place for at least one week after the DNS records changes. I monitor your old server's log files to make sure that the box is really not being used anymore.