Hey @heswebs. As you mentioned, you're already making changes to your theme's child template and files. So if you feel you confident coding in /html/css/php/js, then you could create a new page template and write a custom WP_Query to fetch only the media you want from rtMedia plugin. Creating a custom WP_Query gives you full control of the query parameters, thus making it easier to make both things work together.
An alternative options is the Ajax Load More - Infinite Scroll plugin that allows you to deal with the creation of a custom WP_Query without the need of messing up with the theme's files.
The plugin helps you build your queries through the selection of a few options, such as custom post types, categories, number of posts/items to fetch etc. The free version allows you to create just one template, so it means you're able to build just 1 WP_Query a time. After setting up the plugin you would have a shortcode/ php snippet available that you can place on your page and then it'd load your content through Ajax with the Infinity Scroll behavior.
I've used the plugin once, it is very responsive and easy to set up. About the compatibility with other plugins, you'd need to give it a try and see how it works on your WordPress environment.
Good luck.