Green dot will always give you minimum fuel flow in the descent phase (doesn't matter if you're level or not).
Cost Index speeds assume that you will make a model flight & approach. Descending at the perfect time, and making a constant descent to the runway. In this case you are not. As soon as a you have been given an EAT which delays you, the best course of action is to go back to green dot to minimise fuel flow. (You might consider holding at higher levels to again reduce the fuel flow if possible, eg. quiet airports).
Cost Index = 0 would be more appropriate if you knew as soon as you took off that you were going to have a delay because of a night time jet ban at the arrival airport etc, although it wasn't designed to be used as such, becuase it is a management tool to optimise costs rather than a speed controller. - Hope this helps. CL
Easiest answer: Use managed!!!