Inside Panelizer, is there a trick to formatting image fields?
Although I could swear that I had done this before, I deleted the image in the panel. This time, when I added the image back into the panel, I got image formatter options. Which I set, and the node behaved correctly.

Despite the frustratingly long time I worked on this, it was a non-problem!

AMENDMENT:
When the panel is first created and saved, all of the fields appear in the panel. If the image field is left as is, there are no formatter options. However, if the image field is deleted from the panel and then re-added, then the formatter options appear. This is noteworthy, I think.