Okay, I managed to figure out how to enable or disable comments per images. Here's what you need to do.
Warning: This is not for the faint of heart! Back up your database first, and make sure you understand what you're doing before trying this.
Open up your database in PHPMyAdmin, and navigate to the wp_posts table. Click the 'Browse' tab at the top.
Then, look for the entries that contain your images. I didn't leave captions on any of mine, so "post_content" was left empty. Another way of telling is that the "post_title" will be the name of your image file, such as untitled-28 or cimg1141.
Click the pencil icon at the left of your post. Then, where it says "comment_status", change it from "open" to "closed" (or "closed" to "open" if you'd like to enable comments). Don't use the quotes, just input the word itself.
Note: You can also adjust the "ping_status" if you want to enable/disable pings here, too.
Scroll to the bottom of the page, and make sure it says 'Save' and then 'Go back to previous page'. Click the 'Go' button.
Go back, find the image on your site, and the comment status should now be changed.
I wish there was something to toggle this within the WordPress admin - or even a plugin to handle this. It's going to be time-consuming to edit every image I upload by hand.
Heck, I'd even accept a MySQL query, I just don't know how to construct them.