Routing Help for someone ex-WLG
 

I have a friend wanting to fly from Wellington New Zealand around couple of Asia's places for factory visits.
They starts from WLG-AKL-HKG-TPE-ICN-PVG-HKG-AKL-WLG.
The bolded codes are places don't need to stopover.
My now EX-TA in Dunedin has not given me any CC over this trip so I am looking for a replacement. Far from happy when I don't get what I asked for.
The 2 TA that we asked always said something about limitations with ticketing. I do not know what that is.
If everything becomes too hard. I might just book everything intra Asia in Hong Kong!
Any expert help would be good. Plus PM me a NZ TA.