What I was supposed to do: On old iPhone, BEFORE I transferred my number to a new SIM, I was to go into Messages settings and turn off iMessage.
Since I did NOT do that, and my old iPhone could no longer talk on the network, I instead called Apple Support, asked to be transferred to a support agent to obsentibly purchase a one-time support incident (for $35+taxes) and when I got through (after a while) and the agent asked my if the issue was with my iPhone I said, "Actually, the issue is I want iMessaging to let go of my phone number but my old iPhone is off the network.
She put me on hold for a bit, came back and said, "Ok, we can do that." then asked for my the number and sent me a confirmation code via SMS. I read it back to her and she deleted my phone number from the iMessage back-end. Done. (And no $35 fee.)
While I was waiting on hold, I did try the delete-your-contact-entry-on-an-iPhone-then-power-cycle-phone-then-add-entry-ba ck-in and I found that worked on my wife's iPhone 5. However, that is hardly a scalable solution for everyone who might have your contact details on an iDevice.
So my learning from this is: When you move away from an iPhone, turn of iMessage in Messaging BEFORE you switch your number to a new SIM.
Really there should be an EXPLICIT way to do this from icloud.com or your Apple Support Profile at any time (my iPhone was never registered, so the idea to unregister it from there is not applicable - and yes, I did try registering and unregistering - no dice).