Agreed - your TA is wrong. For the purposes of OneWorld tickets anything less than 24 hours is OK (other tickets - eg awards - have different rules).

I have done something very similar to what you propose with an ex-TPE DONE4 which went TPE-xHKG-SYD-xHKG-LHR-<USA>-xHKG-oCEB-oHKG-TPE where all three of those xHKGs included me having a night at home in bed.

That ticket was booked direct with CX in TPE. Is there some particular reason why you are using a TA and not just going direct to CX?