You'll use "Backup - all files", not "Restore - all files", to copy a Time Machine volume. "Restore - all files" specifically ignores Time Machine backups.
It's likely going to take longer than 20 minutes. I also don't think renaming will do it: you'll need to specifically select the new drive as a destination. It'll do a lot of preparing but should retain the info.
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--Dave Nanian
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