Howdy Meredith,
Good question. It is not possible to do that. WordPress itself creates what are called “Custom Post Type Archive pages” for custom post types. This is not just one page, but a series of pages all of them created by WordPress itself. And these need to be a new page, that can not be embedded in an existing page.
However, you can style the new page to look like the old one, and even include the content from the old one in it. This does require some WP Theming experience though.
Does that all make sense? Will that work for you? Please let me know.
Cheers!
– Brook