I've just spent a couple of hours building the main circuit up on a breadboard and cannot find anything wrong with it. It's working fine here for me. I used the capacitor, diode, resistor coupling setup, as per the later stages, to trigger the Delay 1 stage to give me a shorter pulse than that of the delay itself, though that doesn't affect the rest of the circuit. I didn't add the 2 pulse output timers since I don't have any more 555's!
I enclose a scope shot below.

The outputs are in order:
Yellow, Delay 1
Purple, Timer 1
Blue, Delay 2
Green, Timer 2
I enclose a scope shot below.

The outputs are in order:
Yellow, Delay 1
Purple, Timer 1
Blue, Delay 2
Green, Timer 2


