Characterising an Audio Isolation Transformer
What's the best way to determine if this audio transformer is designed
  with 600 ohm terminations in mind?


Probably the only clear-cut way is to drive one winding from a signal with 600 ohm source resistance and load the other winding with 600 ohm and plot the frequency response.

If you get a decent flat frequency response then that tells you that it is good for 600 ohms in your target application. But it might also be good for lower impedances like 100 ohms. The thing is about transformers is that they aren't suited necessarily to one impedance regime - they will work across a wide range of circuit impedances. However, the lower you go in impedance the more it is likely that higher frequencies will become attenuated due to leakage inductances in each winding.

So, even if a transformer is good for 600 ohms across a flat frequency range of (say) 100 Hz to 10 kHz, it might only deliver 100 Hz to 2 kHz in a regime where the impedance of the load is 100 ohm.

Additionally, with a 100 ohm regime and using a 600 ohm transformer, you might get slightly improved lower frequency response.


  the winding resistances are 40 ohms and 50 ohms (oddly, not quite the
  same).


This might be because one winding is wound beneath the other i.e. the winding wound closest to the core will use less copper wire for the same number of turns.