Prefill email field in Service Desk widget

We are in the early stages of using JSD to capture support requests from our customers.  Our customers will be reporting issues from within our website where they are already logged in (and have an email address associated with their account).

The existing JSD widget looks perfect, except that it requires the customer to manually enter an email address.  This means that some customers will inevitably create tickets with email addresses which don't match the email address we have on record (which then makes supporting their requests harder).

It would be great if there a way to prefill the email address field in the widget (ideally so the customer can't change it)?

Thanks, Adam.

Original question here.