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"Looks like I needs to move fast but big thanks for the advice."
Don't buy any AA miles unless and until you have found the needed award space. AA will let you put an award itinerary on a free, five-day hold, so you can always buy the miles after you put the award on hold.
I trust that you are already an AAdvantage member, as only those who have been members for at least 30 days may buy miles.
If you can get a Citi/AA Platinum credit card, you would get a 10% rebate on redemptions, up to 10,000 rebated miles/year. You would then only need to buy 129K miles from AA for the roundtrip in F: you would redeem for just the outbound first (67.5K miles), and get 6,750 miles rebated to your AAdvantage account. Then, you would redeem for the on-hold return trip.
But finding F award seats on CX or JL might prove challenging. You can search one segment at a time at ba.com, or just call AA. (CX/JL award availability cannot be searched at aa.com).