Parasitic oscillation - where to start?

[Kremmen]

Yep, better.
Hard to say why you needed such a lot of VAS capacitance but the main thing is that it works, i guess. Usually it is under 100 pF or so, but never mind. Perhaps you will want to check the high frequency roll off point if the cap is way larger.
One comment regarding the feedback, which should increase the stability margin perceptibly: the impedance level can easily be lower, since you are not short of driving ability in the output stage. Lowering to 1/10th would be beneficial against thermal noise in the resistors. Otherwise it should work as it is, too.

[GK]

Hard to say why you needed such a lot of VAS capacitance but the main thing is that it works, i guess.

Not at all. The Miller capacitance required is simply a function of the input stage gm (transconductance) and closed loop gain. His original circuit was wired for a closed loop gain of 1. This, combined with the gm of the input stage (as defined by the 500uA tail current) computes to a unity loop gain frequency (ULGF) of approximately 8 MHz with a 100pF Miller compensation capacitor.

Even with a 1nF Miller cap, the ULGF (at ~800kHz) is still too high for the small signal bandwidth of that Darlington power output stage, and the phase margin would still be marginal.

To properly compensate such an amplifier (without having to resort to using a massive Miller compensation capacitor, which kills slew rate, for one) you need to reduce the gm of the input stage. The best way to do this is to add emitter degeneration to the long tail pair.

[Kremmen]

Like i said, haven't analyzed the circuit at all, but yes it was bothering me too and i was coming to the same conclusion.  The input stage looks like it needs tweaking, and the unity gain was a bit worrying. I did notice the lack of emitter degeneration as well but didn't comment since the OP said he didn't want to change his PCB (did that later). Wouldn't be a big deal to fix it, but it is the OP's design and he didn't ask for a design service, so i didn't

[c4757p]

I replaced two of the diodes with cheap TO-126 diode-connected transistors (MJE181), to make it easy to strap them to the heat sinks. I also replaced the emitter resistor in the long-tail pair with a current mirror. All the changes I've made allowed me to reduce the VAS capacitor to 100pF (I'm not going to push it any lower, since the circuit works fine over the entire frequency range). As for an input resistor to ground in case of disconnected input, it will never be disconnected because this is just the final stage of a signal chain on a PCB.

Thank you all for your help! I suppose I could keep tweaking it, but it works fine now so I think I'm going to leave it as is.

[MartinX]

Just after a quick look at the schematic what stand out to me is the BC545/556 driving the output transistors directly, have you looked at the base current of the TIP35/36 in the LT spice simulation?
Most amplifiers have a more powerful drive transistor like BD139/140. TIP35 does not have very high Hfe and the minimum value in the data sheet is quite low as I recall it.