Dr. Yitzchak Meitlis suggests an answer in his book Parashat Derachim, pp. 126-130. Here's a summary:
The Netziv's answer is difficult because the Torah literally says: "But the famine in the land was severe."
Instead he suggests that an answer may be found in the differences of climate between the two countries:
Rain comes to Canaan (what is now Israel) mostly from the Icelandic Low. The winds carry the cold air and reach this area around wintertime, which is why it rains here in the winter. Egypt, on the other hand, barely gets any rain year-round. The primary water source in Egypt, to this day, is the Nile. Egyptian farming is based on canals that are ready to lead water during the rise of water levels from the Nile to the fields. It was only when the fields were soaked in water that the Egyptians sowed their seeds.
Summer monsoon rains in Ethiopia are what cause the Nile to overflow and water the fields. The rise in water levels typically happens around fall, circa Elul-time. During Tishrei and Cheshvan the water flows to the fields and soaks them, and only then are the locals able to sow their fields.
Having explained this, we can now understand what happened during the famine:
The famine started in Canaan because rain didn't fall in the winter. Meanwhile, in Egypt there was still produce because Egyptian farming was based on rain from the previous summer. It was only when the next summer's monsoons didn't come and the Nile didn't overflow during the fall and early winter of the next year that the famine came to Egypt as well. This can be seen in the verses as well:
"And the seven years of famine set in, just as Joseph had foretold. There was famine in all lands, but throughout the land of Egypt there was bread." (Beresheet 41:54)
And only after does it say:
"And when all the land of Egypt felt the hunger, the people cried out to Pharaoh for bread; and Pharaoh said to all the Egyptians, “Go to Joseph; whatever he tells you, you shall do.”" (ibid. 55)
Therefore, the famine first began in the lands around Egypt, and only a later did it arrive in Egypt as well. That means that the famine ended in the same order, too:
During the winter, rains began falling in Canaan, while in Egypt the monsoons would only come the following summer. So only a year after Canaan once again had crops could the Egyptians eat their own crops. In the time between the end of the Canaanite famine and the end of the Egyptian famine, the Egyptians were forced to sell their land.
This explanation helps in understanding the following verse:
"Let us not perish before your eyes, both we and our land. Take us and our land in exchange for bread, and we with our land will be serfs to Pharaoh; provide the seed, that we may live and not die, and that the land may not become a waste.”" (ibid. 47:19)
What good would sowing seeds be if there was no water? Rather, we may say that at this point the Egyptians heard that the rain had returned to Canaan and they knew that in year's time they'd also get monsoon water from the Nile and wished to ready the land.