We run AMIs in three regions. The key point is that regions are completely separated, so you will have to move everything to other regions (via S3) and recreate your security groups etc.
For the move itself, Elastifox is a great help: http://aws.amazon.com/developertools/609
It is more powerful then the Web interface and helps with moving AMIs.
Potential problems that we encountered:
Moving AMIs (the copying) can take hours! So plan enough time for this.
Sometimes we had problems registering the AMI or it arrived corrupted. I am not really sure what caused these issues, but we could always solve them (in the worst case we had to copy the AMI again - did I mention to plan enough time ;)
I took a look around the Developer Guide and API Reference and nowhere in either of them could I find any guarantee that the instance id would be unique among all availability zones.
The only link I could really find online (besides the one you posted) was this serverfault question which includes a post by a guy named 'jedberg' who says he contacted Amazon support and asked whether you would ever get a duplicate instance id. Their response was:
"Instance ids are unique. You'll never receive a duplicate id. However, the current format of the instance id is an implementation detail that is subject to change. If you use the instance id as a string, you should be fine."
Which doesn't specifically say that they're unique per availability zone, and does say that they make a guarantee to provide a unique instance id.
Given no concrete indication either way, I'd err on the side of caution and assume you could receive a duplicate in another availability zone. If you're really not sure, you may want to put a request in with Amazon support to ask for clarification (and post their response here!).
Best Answer
Using the AMI Copy function, it is only possible to copy those AMI images that belong to your account. It is not possible to copy AMI images belonging to others.
http://docs.aws.amazon.com/AWSEC2/latest/UserGuide/CopyingAMIs.html
To get around this, you can: