Transfer existing consolidated billing account into newly deployed Control Tower Landing Zone

You can bring an existing organization into AWS Control Tower, it's called registering the organization, or extending governance to the organization. Similarity you can also register the 7 OU into control tower.

For details, please refers to the documentation at: https://docs.aws.amazon.com/controltower/latest/userguide/existing-orgs.html

No, there doesn't seem to be a way to transfer an existing consolidated billing account with Control Tower. The management account is the billing account in a Control Tower-managed environment, as specified in the docs https://docs.aws.amazon.com/controltower/latest/userguide/how-control-tower-works.html.

You might be able to enable Control Tower in your existing environment (and use your existing consolidated billing account), but I'm not sure if that's guaranteed to work. You might be able to get clarity from your account manager, or via logging a AWS Support ticket.