Hello Jack,
Thank you for your question. You are correct, profile images are now exposed from pbs.twimg.com, which should be seamless by using the profile_image_url and profile_image_url_https from the REST API. We have updated the documentation to reflect the host change: [node:10796].
If you encountering any 403 or 404 errors while trying to access profile images, please make sure to have up-to-date user objects. Indeed, chances are the images moved hosts or the users have changed their profile images; I am not sure how long URLs continue working in that latter case. In any case, the recommendation is to call the [node:10320] endpoint to gather the most recent profile image URL.
Please let us know if you have any other questions or issues.