So, I was actually able to do it with a query string:
post_type=shop_order&post_status=wc-processing
and then use post meta keys:
Order #{{dc:post:id}} - {{dc:post:meta key="_billing_first_name"}} {{dc:post:meta key="_billing_last_name"}} - Date: {{dc:post:date}} | Total: ${{dc:post:meta key="_order_total"}}
{{dc:post:meta key="_billing_email"}}
{{dc:post:meta key="_billing_phone"}}
{{dc:post:meta key="_shipping_address_1"}}
{{dc:post:meta key="_shipping_address_2"}} {{dc:post:meta key="_shipping_city"}}, {{dc:post:meta key="_shipping_state"}} {{dc:post:meta key="_shipping_postcode"}}
Not sure why the date isn’t showing up, however. Everything else appears correctly.