Restore from CCC or Time Machine? I'm getting a replacement Macbook Pro today. I just made a complete backup with Carbon Copy Cloner, and I also have a full Time Machine backup.

Which should I use -- Time Machine backup or CCC -- and how? I want to avoid having to reinstall software and zshell settings and so on as much as possible.
Time Machine would be your best route. Boot the new computer up holding Command + R and then in the Recovery utility, select "Restore from Time Machine backup" - assuming it is a full backup, it should work OK.