Sorry to be blunt, but Brookfield is not correct in this case and neither are you. The Change of Strength (COS) Date is one of the most misunderstood things in the CF. The COS Date is simply a spot on the calendar where you cease to belong to one unit for administrative purposes and begin to belong to another. In simple and somewhat ghoulish terms, it determines who gets stuck organizing your funeral if you die en route to your new location (heaven forbid, knock on wood, etc).
Your Report for Duty (RFD) Date is not in the Posting Instruction, but is actually a more pertinent detail. It is negotiated between the gaining and losing COs to any point within 30 days either side of the COS Date. Any point outside of this 60 day window requires a new posting message. In a standard posting situation (i.e. there are exceptions), once the two units have agreed to an RFD Date, then Brookfield used RFD Date to determine the schedule for packing, loading, starting travel etc.
Keep in mind that you also can have input into the RFD Date. For example if you're in a situation where you can break a lease at COS -20 without penalty, then it's in everybody's best interests to move your RFD date forward and move you well in advance of COS. This is possible and should be encouraged. You could even have the move completed before COS. By the same token, if moving the RFD to COS +20 means your kids can finish school before you leave, that makes sense as well. Brookfield shouldn't care one way or the other what your COS Date is. They only need to know the RFD Date. PM me if you're still having issues.