Ahhh, sorry about that. I got the wrong end of the stick there.
Hopefully Willam will pop in here and advise that what you want is easily done using a script. If not, your only real resort is to do the renaming manually.
I'm a bit surprised at seeing the report about the generation process changing the file names because to my knowledge, the only time that should happen is if you used that "convert to lower case" option.
Too bad there isn't an option to choose whether things are converted to upper or lower case. You might want to suggest that to Adobe via the link below:
There are various tools around that can be configured to change file names in various ways including the case of an extension only. I would guess if you used one of those Rh would continue to play nicely as it is on a Windows machine but the output would have the right case.
Test with a copy project or a dummy project. You might need to delete the CPD before reopening the project after renaming the images.
See www.grainge.org for RoboHelp and Authoring tips
You can try this link. This is seems to be the less complex one.
Hope it works.
Note: Since, you have Photoshop, Bridge would comy by default.