There is a website with a photo of the Chattanooga with another steamboat directly behind it that may be the Paint Rock. The site that has these pics also has pics of several other steamboats that are indentified but none are the Paint Rock, at least none I can figure out. Here's their link...

http://chp.mtsu.edu/tncivwar/steamboats/transport_chattanooga.html

I'm gonna try to email them for help.