Yes, you can do the move described in the first post (move, then load, then offload).
I believe the theory behind not allowing transports to offload in two territories is the fact that deployment into significantly different areas will take time. For example - if you have a division in Alaska, and another in Western Canada, and there are no enemies nearby, you could meet up halfway and get on a transport. But if you are on a transport and offloading, that transport would have to sail to a different region to offload troops in any geographically significant other location. So FUNCTIONALLY, the transport can only offload into one territory.