Hmm. I forgot this unit was an early prototype that I only had running at 20V. This is a split-rail design using TLE2426, with a 9V battery supply with a DC converter, it gets a bit unhappy with extreme loads, especially this early version. So I imagine a more robust power supply could do better.
Anyway, I didn't have a 600 ohm load handy, so I used my trusty Sony 7506s (63 ohm) instead. The amp also has a 150 ohm series resistor on its output, so that's 213 ohms. I measure almost exactly a 10dB drop at 1kHz at the headphones, which works out to . . . like 0 ohm output impedance. Probably Sony isn't 100% accurate on their spec, but it seems that INA217's output impedance is sufficiently low.
This circuit can do 6.6VRMS at low distortion with the 21V supply (<0.01% THD) into no load, that gets about 2V from the rail, I recall the 32V supply version I have does 10VRMS, which is about the same.
Into 213 ohm, I managed 2.4VRMS at low distortion, for RMS current of only 11mA (peak of 30mA). But at that point, the power supply was sagging down to 36V (from 45V).
Still, worst case based on those results is 11mA, so that's at least 6.6VRMS into 600 ohm. I'll see if I can try that tomorrow.
One consideration is that if you really want to drive an output hard, INA217 is single-ended and you really need the free 6dB from a following inverting stage. I'm not into high headroom anymore, I like very low power consumption and my target is -10dBV input converters.