My server is currently running PageSpeed version 1.8.31.4-4056. In our pagespeed.conf file, I see the following entry:
# Many filters modify the URLs of resources in HTML files. This is typically
# harmless but pages whose Javascript expects to read or modify the original
# URLs may break. The following parameters prevent filters from modifying
# URLs of their respective types.
#
# ModPagespeedJsPreserveURLs on
# ModPagespeedImagePreserveURLs on
# ModPagespeedCssPreserveURLs on
Looks like if you uncomment the last three lines, the URLs will be preserved. You'll then have to restart Apache.
I found some documentation about the settings here: https://developers.google.com/speed/pagespeed/module/config_filters#preserveurls
Unfortunately, preserving URLs disables some other useful features.