wouldn't it just be simpler to use a resistor, cap, general transistor and a normal relay?
The idea is that while the cap is charging it is taking all of the power, so the relay will not close. Once the cap has finished charging, the relay will close and remain closed until the power is cut off, at which point the relay will remain closed until the cap discharges.
You can change the amount of time before the relay closes, and the amount of time the relay will remain closed after power is turned off by changing the values of the resistor and cap.
The type of relay in either circuit is not important.