{{layout}} handle in email

Question

I am trying to display cart contents in the stock EE abandon cart email.

The challenge here is that the email doesn't seem to have the same access to the quote as similarly formatted order emails.

Ideally I can do something along the lines of:

{{layout handle="sales_email_order_items" order=$order}}

Though, obviously, with the relevant quote to the email being sent. How would I create a rewrite that would set access to the $quote?