I'm still having trouble thinking about how the capacitor is charging and discharging current paths which is key to how the flashing is supposed to happen. There's a lot going on in that little circuit.
Question: Since you didn't build it with the LED chain, did you use the same resistor values? Or did you modify them to account for the fewer LEDs? With fewer LEDs the resistor has to be higher. YOu must have though, or else the LEDs would be very bright just before burning out (assuming the circuit is actually doing what it's supposed to be doing), which you say they aren't.