Looking for advice on the best use of ~1M FF miles/points to get my family (wife, son & daughter) to/from Australia for Christmas and New Years this year.

Am starting in the AA forum as this is where the majority of the miles are.

AAdvantage: 660k mi

Also have:
United: 250k mi
Amex: 125k points
SPG: 100k points

Have been hoarding miles for sometime for a family vacation to Australia this Christmas. As this week, we entered the 10 month advance booking window for award travel on American to/from Australia and have found multiple round trip routes that consume all or most of the AAdvantage miles.

The goal is to book 3x round trips from LAX to SYD using as few miles as possible - departure no earlier than Dec 2017, return no later than Jan 4 2018. Original hope was 1 pax in business, 2 in coach but the miles required are forcing this to be 3x in coach.

I will purchase my own ticket as I will need the EQMs towards retaining PlatExec on AA - knowing they will be split between 2017 & 2018 on outbound and return.

All tolled we have over 1M miles/points across AA, United, Amex & SPG/Marriott. Before committing booking for the 3 round trips, just looking for advice as to going the longest distance for the fewest miles possible. Are there any situations where moving/converting miles from one program to AAdvantage makes sense and/or should 1 pax travel on United using those miles?

Thanks in advance for suggestions, tips, etc...!