> I'd like to eventually make this a line stage that could drive 600 ohm inputs or phones without needing a xformer.
Why? That's like asking a greyhound to pull a sled. Some jobs are more suited to a mastiff.
Certainly whatever sweetness Darling found in this tube, working at high impedance, will be lost (at least totally different) with a low-Z load. There are several tubes that would strain less with low-Z loads.
Sure, you can do it. Peak current will be about 18mA, barely enough for +20dBm or 100mW in 600Ω. Put in a transformer, you could do 10 times better, and at lower distortion.
Working almost to current-clipping in a low-Z load, you will get around 5% THD, instead of the 1%-2% THD you get working into a hi-Z load at reasonable currents.
> Not as a grounded cathode of course.
GC is always best for power gain. When you have power gain, you can trade-off for lower distortion, wider bandwidth, whatever.
One extreme tradeoff is cathode follower. Power output is unchanged from a GC stage with the same current and voltage, voltage gain is lower and distortion is lower by the same amount. Simple feedback, but the simplest voltage feedback possible.