Better semiconductors generally make oscillation worse, not better, because of the increased bandwidth. This is why the "improving" opamp equipment with new devices usually results in oscillation as the slew rate is 10x the original. A new transistor is good to 50 MHz, while the old ones struggled to hit 1 MHz frantically flapping their wings. Old and slow is the order of the day.
I suspect the big issue with the SWTPC stability is Muntzing plus a lack of simulation plus a lack of zeitgeist to diagnose the issues. A Zobel on the output devices, or perhaps some resistors to lower the Q for > 20 kHz, should stop the oscillation, and the feedback loop may have poor stability which can be improved. I haven't simulated it, but I was going to use Pete's spice model for the Tiger, suitably updated for the Plastic Tiger's characteristics and the Class A bias.
I've seen similar Class A headphone amplifiers which are rock stable. So the design needs some study.
It's a back-burner project, but I'm periodically reminded to bump the thread in case a new member says, hey, I have that manual!
Your caution, however, while known to me is nonetheless appreciated as if I didn't know about either the oscillation issue or B+ on the rails could/would result in a blown pair of cans. Always worth pointing that out. Many headphone amplifiers have marginal designs. I have the Ramsey portable headphone amplifier which I must rebuild to remove oscillation, and improve linearity and transient response. It's destined for my shoulder bag to be used with an inexpensive pair of cans; if it gets stolen or fails I'll not be out too much.