I could be way off base here, but it may be that your proposed itinerary exceeds the MPM (Maximum Permitted Mileage) from the U.S. to Australia. If your award is subject to MPM, this would be based on the most direct routing, from NYC to either LAX or SFO then onward to SYD.

For example, the MPM for JFK-LAX or SFO-SYD is 11,947. However, you use up 11,734 of those miles just to go from JFK-FRA-BKK, with over 4,000 miles still left to travel from BKK-SYD. This would put you way over the allowable mileage.

To overcome this issue, folks often have to book two award tickets to stay within the MPM for each portion of the trip. That may be why CO is stating you need to combine two awards, not based on class of service so much as staying within MPM.