Re those United flights:

LAX-SYD July 15: first class 12-4-4 (12 seats, 4 booked, 4 standbyes); business 52-30-0; coach 310-319
FYI SFO-SYD: 12-2-2; 52-23; 310-343

SYD-LAX July 26: First 12-3-0; business 52-29-0; coach 310-268-0
FYI SYD-SFO: 12-1-1; 52-16-0; 310-281-0

It looks like you "should" be able to get out and back if they are eligible for business, not just coach.

FYI, I also checked the 8th and 19th for comparison purposes. There are seats in first and business, outbound coach is oversold, and return coach has less than 25 seats open on both flights to SFO and LAX.