Adding New Fields to Help Scout Submission
In the below example a new field is added to the support ticket submission for via the hd_form_message hook. After the submission the conversation is filtered and the field is added to the message body.
Adding your custom fields to the message body is the only viable solution since these "conversations" are essentially emails, and tags are used for the conversation type. You can learn a bit more about this via the Help Scout v3.0 release post.