I don't think you'll be able to get any award seats in economy back from the US in early October due to those dates coinciding with the end of Australian school holidays so that rules out the 140K award ticket.
Re the paid option - you don't necessarily need to buy a 'round world fare' as such as your itinerary is basically a MEL to Europe return airfare with a stopover on the way back (NYC) so the routing would be half via the Eastern hemisphere (EH) & half via the Atlantic/Pacific (AP).
Both of the above options need award seat availability irrespective of whether it's a non points earning award for 140K or a JASA, YASA etc as they still book into those same award buckets. You're going to get stuck when it comes to flying back from the US unless you can return late October, however I don't think that's an option for you.
I think your only real options are either:
a)
QF Classic Award Travel in economy Fri 13 Sep MEL/DXB on QF9 connecting with QF1 Sat 14 Sep DXB/LHR (only transit in DXB no stopover required) which will be 64,000 points plus taxes of AUD306.02 per person which has availability of at least 4 seats.
Then buy a one way paid ticket CDG/JFK/MEL in economy based on flying AA45 CDG/JFK on 01 Oct then AA7366 (QF108) JFK/LAX then AA7356 (QF94) LAX/MEL on 10Oct arriving MEL 12 Oct. Airfare AUD1392.02 taxes AUD676.62 booking fee AUD10.00 total AUD2,078.64.
I used the website
www.jetabroad.com.au which I find helpful as it’s one site that allows you to price one way and return airfares combinations with a stopover which a lot of other airline sites will not. It will also price open jaw itineraries. I have never bought a ticket through these people, only used their site to price itineraries.
Alternatively, could always buy some Avianca Life Miles and do a J class award coming home CDG/JFK/MEL as they do one way award redemptions for half the return level (unlike USDM who charge the same for a one way journey as a return). It’s worth enrolling now in their program because you need to be a member
prior to them having any bonus buy offers. Personally I'd just enrol now & wait until their next bonus points buy offer.
OR
b)
A paid ticket for all 4 of you in economy class & using
www.jetabroad.com.au flying QF9 MEL/LHR on Fri 13 Sep then the same flights as above CDG/JFK/LAX/MEL would cost AUD2,356.20 for airfare, AUD873.92 taxes, booking fee AUD10.00 total AUD3,240.12 per person.
If travelling on OW carriers you could always credit these flights to AA’s Aavantage program to get some points in the AA camp but double check the booking classes/airlines for these paid flights would earn points on AA.
I wouldn’t bother having one person in J as you’re better off travelling in the same cabin particularly if SWMBO is a nervous flyer. Now that you have the knowledge of USDM, Aadvantage, Avianca Life Miles etc, I would plan ahead for the next trip giving you plenty of time to book a premium award on your preferred carrier on the dates you need.