I have a solution if anyone else encounters this. It is an issue with the mod_pagespeed script, and Google actually came up with a workaround, and a future solution.
Here's part of what one of their developers told me:
The rest of the message dealt with other suggestions about the WordPress theme, but this is the important stuff, also that the version of mod_pagespeed used here is about a year old and sadly in need of an update.
I used the .htaccess directive: ModPagespeedDisableFilters rewrite_images
It worked. I have tended to be somewhat wary of Google and privacy issues in discussions on my radio show and in my online columns. I feel somewhat better about Google after their quick responses to my problem.