Moving off of a FQDN should be possible without reinstallation, but it will not be easy.
Content databases can be detached from and reattached to SharePoint with the correct server name. For service application databases it's a bit more difficult but perhaps Rename-SPServer can do the trick. You could use the configuration wizard to remove the server from the farm and then add it again but pointing to the NetBIOS name for the SQL server. Testing will be the key here I'm afraid.
In any case, a good practice is to create SQL aliases to have more flexibility in the future. You can refer to Move database to new SQL Server for information.