What is the cause of this drastically different simulation behavior with slight variation in capacitor values?
a) the circuit as I drew it, is essentially unstable (as a triangle
wave generator).

Correct. With both op amps acting as amplifiers with positive feedback the result is a bistable circuit that wants to lock up in one direction or the other. To work properly the integrator + and - inputs should be swapped around to produce negative feedback through the capacitor.

b) a finer step in the simulation allows a longer time before the
instability becomes apparent.

It seems so.

c) I just happened &quot;get lucky&quot; that the instability was apparent after
5 cycles with the 5uF capacitor, and not apparent with the 5.6uF
capacitor within 10 seconds.

Yes. the overall positive feedback should cause it to immediately lock up to one supply voltage or the other, but a simulation may be too 'perfect' to show the instability.
When I tried your circuit in LTspice both op amps stuck 'on a knife edge' at exactly zero volts, until I added a tiny bit of noise into the circuit to push it 'off the knife edge' and lock up. If I turned on the option &quot;Start all DC supply voltages at 0V&quot; it acted correctly.