Hi,
For this you can follow your approach of re-signing with RootCA for Server A, this is same process as if you are renewing a expired Cert or renewing before it is about to expire.If you want to use old cert you will have to revoke and remove the new Cert, this might be messy so I will not suggest or agree with this approach.
Note: Always Backup the CA DB and Logs, also note down the steps you are trying to implement in Prod Env and proof read for sanity check.
Hope this helps.
JS
==
Please accept as answer and do a Thumbs-up to upvote this response if you are satisfied with the community help. Your upvote will be beneficial for the community users facing similar issues.