sliding block puzzle is a nice description.
So how did you do it? Can I safely create a 'dummy' live account on live.com, or will that automatically create a gamertag for me? Do I have to do it through hotmail.com?
and do I then have to wait 30 days after creating the dummy account before I can transfer to it?
Ugh, let's see if I can remember the steps.
I had a Gamertag attached to an email address that I didn't use. I wanted to attach that Gamertag to my current email address. What I did first was create a Live account with my "real" email address. I then logged into Xbox Live with that Live account, but that was a mistake. Logging a Live account into Xbox Live's website automatically generates a Gamertag. Now I had two Gamertags: my "real" gold account which was tied to an old email address and this new silver account that had automatically generated upon logging into Xbox.com.
The "real" account couldn't be transferred to the good email address because it already had already been associated with a junk Silver account.
Good gamertag - old email
Bad gamertag - good email
I created anotther Live account.
Good gamertag - old email
Bad gamertag - good email
No gamertag - junk email
Now for transfarring.
Bad gamertag to junk email
Good gamertag to good email
No gamertag to old email
I found out how to do this through MS customer service. This is literally their prescribed solution to the problem. As I understand it a transfer can only be done once every 30 days, so if you screw something up then you need to give up and come back in a month.
Madness.
TL;DR: you need extra Live accounts with no Gamertag association for shuffling purposes.