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The other possibility is that it could be something hardware-related, specific to your Mac Mini. I think that through contacting Apple (as you have done), they should be able to tell you pretty quickly if this is something that has happened to other people. If they give you the "huh?" treatment, you may want to take the Mini to a Genius Bar and see what they say.
 
OP:

I suggested something in post 4 above that you ignored.
I will suggest it again:

1. Take an external drive that is intended to be a bootable backup.

2. Initialize it using Disk Utility to HFS+ with journaling enabled.

3. DO NOT partition it.

4. NOW use CCC to do a clone of your internal drive (you're booted up from that, right?) to the external. NO PARTITIONS involved.

5. When CCC is done, try booting from the external.

What happens?
 
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