Difficult op-amp/phase shifter question, simple circuit

[ChainsawFuzz]

From the beginning...
The MXR Phase 100 has four non-swept phase shift stages, along with six swept stages. I breadboarded a stack of these (12, 3 quad op amps, 20k inverter resistors, 30k RC resistor). Worked great - as it should, it's a string of unity-gain phase shift stages, barely more complicated than inverters or non-inverting buffers. By itself it does nothing audible to audio.

Insert it in series with the swept stages in a phaser, before the phased and straight signals are mixed, and it's like a street kid/finishing school switch. In my case it was a Small Stone. It's a crude, brash, easily identifiable phase shifter sound. Add this circuit, and suddenly it sounds sophisticated. It's still recognizably a Small Stone - the color sounds right, and the sweep is the same, but the background is different.  It will also make flanger feedback neither tubular nor metallic, but an odd mixture of the two, but that's for later.

Cool. So I built an add-on board with 3 TL074s. Really clean simple layout, power busses from one end to the other between the IC leads, bypasses at every IC, nothing but a string of unity-gain stages with really short wires between components.

Fire it up - no signal. DC levels are fine, signal tracing shows two working stages, three progressively weaker stages, and nothing beyond that. Touching a non-functional stage's output while trying to listen to it disclosed the sound of ultrasonic oscillations and beating. Massive ultrasonic oscillations. Nothing I tried made them go away, or made the circuit work. Except swapping out opamps, to pretty much ANYTHING else, from a 324 to a pair of 5532s on a header.

I encountered, but can't find right now, an article talking in depth about that weakness of the TL0xx op amps. But the article didn't ask my question.

My question is - is there any way from the op-amp datasheet that I could have predicted this behavior BEFORE building the circuit? All I can see is that it has relatively high-value resistors - 128 ohms and 64 ohms - in series with the output, rather than raw emitter followers. But the load it was driving was utterly simple, with no particular capacitive loading. There wasn't any reason to think a TL074 couldn't drive it.

[Aleph Null]

TL0XX opamps can lock up from high-gain oscillation in ultrasonic and subsonic ranges, but I wouldn't normally expect that in a buffer/unity gain setup. Can you provide a circuit diagram?