totally up to you and your bank processes.
There's no requirement to start over ever, at least none that I recall reading.
The borrower is counter-offering you to remove the co-signer.
You are accepting.
It's not changing any of the three items that require a new CD to be done so I think you can just take the co-signer off and close as scheduled.
If I'm off base, I'm certain someone will chime in and let us both know.