Welcome to Flyer Talk and the United forum.
As alluded to above, there are quite likely Economy Plus seats available for your flight. You just can't see them online because the website only shows them to users who are "qualified" to purchase them. If you will provide date and time of your flight, we can look that up. Assuming there are seats available in E+, you may wish to consider purchasing the Economy Plus Access Pass from United. It is a bit pricey at $349.00 but will give you access to those extra inches for any United flights for a full year, including your planned trip to SYD. You are about the same size as me and I can tell you E+ makes the difference between a tolerable transpacific trip and real agony.
It is possible that you would be able to purchase iindividual segment "upgrades" to E+ by calling United or at check-in for somewhat less than the $349.00 total but the E+AP is the only way I know of to guarantee E+ seating for all segments in advance (assuming it is available.)
JR