Sounds like an opportunity to use "expertflyer" and check the availability on the flights for both native and codeshare fare buckets.

One of my very early attempts with the RTW desk had ticketing rather closer to my flight dates than I now prefer. The answer was no seats in the codeshare L class buckets were available.

And the answer at one of the (physical as in an office open to the public) Qantas reservation desks was that their system doesn't display the code share choices. Can't book if can't display. I suspect telephone reservations has more flexible display options.

YMMV

Fred