OK, I found some 1458s. The first circuit does not work with this op-amp, but it _does_ work with LM358 (same pinout) !
I also tried my favorite TL082 and it does not work with that one either. But it works fine with LM358.
(I did not try the variable setpoint voltage divider using the 100k pot, I simulated it with two 47k resistors, with the Pin 5 from the midpoint. With these values it triggers with 10R but does not trigger with 22R between the test leads. )
I'm using a BC337-25 transistor instead of the 3904, and an LED+resistor instead of the buzzer, in a low-side switch configuration. (Led Anode at +9V, 1k resistor from LED Cathode to transistor Collector, Emitter to Ground, Base to Pin 7 as usual.