Just put an extra blank line before the details tag, and the images will hide properly. Props to @EricF for the how-to-use-the-forum thread where I learned that.
Edit: Also, seriously nice solution. I might have to do the same for my non-travel set. I’m still trying to find binder pages I actually like though for the extra play folders for my travel set, which will likely make an update to the main post (because I have three different types I definitely don’t like).