Here it is SEVEN YEARS LATER, and I'm finally posting an answer to my previous question.
The solution is NOT OBVIOUS.
When you try to change the image in your DeviantID widget, it only allows you to pick images from your DeviantID gallery. For most of us, that gallery is EMPTY. Why? BECAUSE DEVIANTART NEVER TELLS US ABOUT IT.
SO: select an image you’ve already uploaded to DA, open it and EDIT it into a the category "DeviantArt Related >> DeviantID"
Now it should show up as an option when you make changes to the DeviantID widget.