You need to make sure the USB drive is properly partitioned (as GUID) before you back up to it. Then, make your "Backup - all files" and try starting up from it.
And when you install the new drive, you'll Option+power on to start up from the backup, then partition the new drive, use the same name as the original, and restore as explained in the User's Guide. No OS install is needed.
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--Dave Nanian
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