How do I give permissions for a custom header image only?

Hello,

I would like to allow for my site registrants to be able to upload and place their logo in their site header instead of the default h1 header text. I've disabled all customization options at this point because my company's project is enforcing strict style guidelines (in years past we've had people completely blow out our themes). So, as you know, that means all customization menus are gone, including Header.

So, I'd like to give our users the ability to upload their logo at the top of the Twenty Twelve content area instead of the h1 text. Is this possible?

FYI, I'm using 3 child themes based on Twenty Twelve. If you need more info please let me know!

Thanks in advance!