Hi, @sptramer. Any API endpoints used via the web UI can also be used directly. We have a support guide that covers how to examine the API calls in the browser devtools here:
Using that workflow you can see how the API call is made (the URL format for the endpoint) and examine the format of the JSON being sent to delete deploys.
Once you have the example API call and JSON format information, it will be possible to both call the API to get a list of deploy ids to delete and also to then iterate over that list of ids deleting the ones you want to remove.
Using the API directly in this way is both permitted and encouraged. It does not break our terms of use to directly call the API.