Figured this one out, it appears.
If I use the same images for both perpixel & nonperpixel logoff & shutdown backgrounds, respectively, everything displays correctly. I had nonperpixel images set for the "regular" images - appears that's where the small square backgrounds were coming from. Deleting the "regular" images did not work, actually made things worse and affected the shutdown dialog buttons as well, but once I selected the same images for both "regular" & perpixel for each, they displayed the buttons correctly.
One down, two to go.
Thanks to Cavan1, Bichur & Saga Gemini for your help.