Firstly you say full subscription, what package do you have; Original, Variety or Family?
Secondly, you say you thought Sky Go Extra was included free, why so? If it is because you have multiscreen you still need to activate the free Sky Go Extra.
Thirdly, as Annie has said, you can only make one device change per month, so whatever you do, do NOT remove all your devices. Once Extra is activated, you will have 4 slots available (two new ones in addition to the two you already have) so will be able to add the new device.
Once Extra is active, you will be able to download programmes for offline viewing.