I managed to solve it.
I was about to suggest I just send you the APK to test yourself. Before doing that I thought I'd check that it reproduces when I copy it onto the file storage via device bridge and found that it works correctly.
I then had a look at the Assist App download and noticed that it's mimetype application/vnd.android.package-archive and our apk was just set to application/octet-stream I changed that to match your app and it now downloads and installs on the device 