Yesterday I did build the circuit (low power version). It actually worked the first time.
I did not use pushbuttons: instead of the S1 and S3 button, I simply touched the 15K - 2K2 connection with a wire to 5 volts, and instead of S2 and S4 I used a temporary wire to connect the low side of LED2 or LED4 to ground. So the 3K3 resistors connected to S2 and S4 were also not used.
The LEDs that I used did not respond well to the 0.5mA that th circuit provides. Raising supply voltage to 6 volt brought some more light (at 6 volt the circuit also worked well).