This issue has been resolved. The app was not deploying to App Store Connect because of a corrupted icon.icns file.

I had two icon.icns files in my app bundle, one was good and one was corrupt (only 8kb). The icon specified in the package.json changed from the good one to the corrupt one. This caused the app to stay stuck in processing when trying to upload it via Transporter - no error message was provided by Apple indicating the issue, so it took a while to track this down. Not a very good developer experience.

Hopefully this helps other people who are experiencing a similar issue with Transporter deliveries getting stuck in processing.