I think AS doesn't offer one-way awards, so AS points for business award in both directions were deducted, with a voluntary downgrade to PE. This is presumably what the OP means by "paid business ticket".
The OP's beef is entirely with AS; and they are very adept at customer relations, so he continues to love them despite being screwed by AS. QF does not receive payment from AS for business class travel LAX-AKL, instead AS pays a lower dollar amount for the PE ticket that AS issued. This is why QF doesn't want to pay for J lounge access at LAX for the OP; now if AS had paid for J instead of PE, it would be a different story. Of course AS would counter that it is happy to pay for J instead of PE, but QF won't accept payment. QF does have a set formula for releasing award seats, and empty seats go for other purposes first (e.g. being used for upgrade would generally take precedence over being used for additional awards).
Now the OP should be happy that he paid so little for his award tickets on QF == AS has the cheapest redemption costs of any FF program right now. Unfortunately these cheap partner awards also come with restrictions, like the poor service from AS that he encountered. I fly a fair bit with AS as well as QF, so I think I know exactly what transpired. Frustrating for the OP -- understandably so -- but ultimately this is an AS problem and QF was just following the rules while AS was not (or misled their customer).
Edit to add: all airlines transfer flights to gate or airport control at a certain cutoff time; after this time, no changes can be made by the central reservation system. AS was quite capable of contacting the QF person controlling this flight, but chose not to do so. A tip for the OP: next time, walk over to T3 and ask the AS agent at their F check-in to help you ... some excellent senior agents work for AS at LAX and they would have known the phone number to call at QF to get the seat reassigned by QF, and the ticket reissued by AS. Too bad AS 800 number didn't know how to do this or tell you this little bit of advice.