Yep, we are lucky! There's no magic document that will speed up processing, so stop driving yourself nuts.
Original Nationality: US
Visa #1: PMV (300) through Washington, D.C
Applied: April 2013.
Visa Granted: January 2014.
Visa #2: Subclass 820 (From PMV).
Applied: End of April 2014.
Visa Granted: Early July 2014.
Visa #3: 801 (PR)
Eligibility Date: End of April 2016 (Applied a month prior).
PR Granted: Early April 2017.