By introducing multiple copies of the same energy system, you just triggered a new idea: You could have additional copies for the two extreme FCR cases, one with 1 MW of additional supply (negative FCR) and one with 1 MW of additional demand (positive FCR). This is not what would actually happen but the 1 MW could happen at any time within the four hours and your system needs to cope with it.
Your second option almost sounds like the second option I originally named, except you have different values for the upper bound and the lower bound. I think this is the more efficient way but it is also more restrictive. You could just force the battery to leave 1 MWh margin to both, its full capacity and its empty state, for the four-hour blocks where you provide FCR. Done.