I just ended the first part of a similar RTW (BUD to LAX) - i was able to get it still for the old price (HUF1666400 - approx 5500 USD). My routing is/was:
BUD-LHR-MEL-XSYD-NAN-SYD-XHKG-NRT-XTPE-XHKG-DPS-HKG-LAX-XMIA-RIO-SCL-UIO-XMIA-JFK-XCHI-SNA-XCHI-FRA-XLON-CPT-XLON-BUD.


My travel agent mentioned that after i bought the ticket the rules have changed slightly and i would not be able to do the same again.
First, there is a rule that you cannot transit one city more than twice (in your case HKG), also you need to to LON-SYD on one single flight number.
Also not sure about more than two intercontinental departures from the US. Is this possible now?
Also, it looks like you have too many segments in europe.