Ninny's got the best idea, I think.
If you're staying on the same server cannot you just bind the new name servers to the old IP?
When I changed name servers for my VPS. I had 4 IPs, I kept the original name servers (ns1.olddomain.com& ns2.olddomain.com) then just added records for ns1.newdomain.com ns2.newdomain.com bound them to unused IPs.. Updated the record at the register... Waited a couple of days, updated all my domains hosted on that server to the new name servers waited a couple more days and deleted the ns1.olddomain.com & ns2.olddomain.com.
That is assuming you have a couple of extra IPs to work with.

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