RTW
I can recommend both the Star RTW and ANZ. Used both more than a few times. You probably saw Star RTW is done on miles and Oneworld RTW is done on sectors and continents. If you calculate your miles you can work out potential side trips from HK to use up the miles you have spare before you enter the next mileage bracket. Japan would be my side trip of personal choice out of HK.
Star are good at RTW, I have called my travel agent with an itinerary on the way to the airport and had the ticket issued by the time I was in the checkin queue. OW are not so quick as they have a validation process to check the fare rules that can take up to a day. Your agent should advise you which airline ticket stock it gets issued on, can't remember the rules about who, might be first carrier in the itinerary but worth asking as that is who will become involved if you have a refund or other money query.
The star calculator shouldn't force you via FRT - you may have it left in as a destination ? Selecting LAX should offer the ANZ-LHR option.
Used the OW calculator many times, never had the problem you describe?
It's worth a detailled look at the rules to optimise side trips. Hope this all helps