Unfortunately WordPress doesn't let you change permalinks of custom post types, but you could try a plugin like this one: http://wordpress.org/plugins/custom-post-type-permalinks/
Thanks so much for your response! I'm wondering if this also is causing the reason I can't "preview" any of the posts I make via custom post types? Does this go hand-in-hand?
Actually that might be a separate issue - not sure. I've had a few other people report that and I've looked into it and haven't been able to find a solution yet. I don't know whether or not it's from a theme-related thing, a plugin conflict, or a WordPress bug...
I looked at the screenshot but I'm not sure what's generating the image link - it's not something in the theme that I'm aware of. Did you try with all plugins completely disabled and using an unmodified version of the theme to see if the same thing happens?
Unfortunately the Custom Post Types Permalink plugin did not work. What I've started doing is marking my post as a post rather than in a custom post type if I need to change the URL and then changing it back to the custom post type after I've changed it. After googling quite extensively, I've still not found a 100% solution to this particular problem.
As far as my image issue that I mentioned, I have no answer to that still. But I've managed to get my website back in first place in Google, so I must be doing something right.
I appreciate all the help, Brian!