This is the answer I gave to you in the other post you posted to.
Even if you are booked through DVC you can make online ADR's. There is no system override required. You do not need to call DVC directly.
I think your problem is, as you state, you have 3 different reservations.
Each one of those reservations can only be booked + 10 from the first day of the individual reservation. That would be true even if you booked a hotel room with Disney. It doesn't matter to the system that you are staying consecutive nights, you have reservations that begin and end.
And no, you can not call DVC. Only Members can call Member Services. But as I explained, the member does not need to provide their credit card number. You just need to call on the first day of each reservation.