Thanks to this post (https://itch.io/t/5408218/game-jam-api-to-fetch-basic-jam-info) from about a year ago asking about APIs for game jams, I found a way to get a JSON output of the game jam entries which should suffice for what I need.
Structure is: https://itch.io/jam/[Jam_Id]/entries.json
You can get the [Jam_Id] from the browser URL while editing a jam that you are a host of. It appears you can also get the id from a jam's public view by searching for "id" in the inspector:

Here is an example from the Business Card Jam I co-hosted several years back: https://itch.io/jam/12002/entries.json























