This morning on my way to university I was listening to it and I realized something: The two solos represent the battle that takes place in the song. Let me explain myself:
The first solo comes after the "Legacy" section, which was also precedeed by the riff that has this "proudness" feeling to it. And it comes before the instrumental part in which the song turns into a "conflict", just before the second solo, which is followed by the lamentation and desperation. First solo is about the crew, the ship fighting the storm. Their resistance and wanting to survive. The second solo is the storm raging around the ship, a force of nature beyond good and evil that sets destruction no matter what.
At least that's the way I see them when analyzing the song's structure.