Regarding that latest schematic, I think a capacitor at the voltage sense divider could have larger resistors and a capacitor to ground slowing the response time. In the one I already hot glued together, it has a 100Ω resistor and a large filter cap to sort of do the same, but nowhere near as good. If the one I built don't behave correctly, then he can toss it and I'll buy another box of altoids.
Why do you want a slow response time?
There is no capacitor at the sense divider, in any of the schematics I've posted.
The problem with adding a delay to the voltage sense divider is it will momentarily activate, triggering the alarm, every time the power is applied. C2 ensures, when the power is first connected, the reference voltage is much lower, than the sense divider.
U1d is simply a bistable. When U1a's output goes low, C3 AC couples the negative edge to U1d's +input via D1, which ensures it only responds to a falling edge. U1d's output will go low, turning on Q1. C4 performs a similar function to C2, in that it ensures U1d's output is high when the power is first applied.
To add a delay, C2 will needed to be increased and a capacitor added in parallel with R9. The values will need to be carefully chosen to ensure the sense voltage is always higher than the reference, during power on.