It doesn't appear possible. Even the batchUpdate you reference is for deleting items off of a form, not for removing responses. For the moment, I think you are stuck deleting responses one at a time.
Unfortunately, it seems Google Forms has been the laggard of the bunch to get Apps Script integration and support.
One thought that just occurred to me is you might be able to include a webapp portion in your script with a published url. Then instead of having to make a bazillion REST calls, you could simply pass an object containing the response IDs to the webapp, and it could then iterate over it and run like a regular Apps script on the backend. So instead of a typical doGet() function, you would use a doPost() function that receives your object, and you could use a REST-like HTTP POST request to the published URL. Then iterate over the object and delete each item one by one. --I hope that makes sense.. I'm thinking as I type, and since you are already familiar with REST, I'm guessing the above makes sense to you.