How did the depiction of the swamp bayou as peaceful, beautiful, and as a place of refuge act as a political commentary in this piece?
The best way to answer that is probably to look at the perspective of the artist himself. Meeker was born and raised in New Jersey, but was deployed in a Navy Gunboat in Louisiana Swamp country during the Civil War. So his viewpoint was that of a Union soldier captivated by the natural beauty of the region.
By applying a traditional, Hudson River School style approach to the landscape, he focused on the light and nature before him. This created a swamp viewed more with awe than fear. It's not so political as it is a different perspective on a region many saw as sinister and foreboding at that time. Though you are right in that many Hudson River artists saw the natural world/frontier as a refuge from the complications and corruptions of the civilized world. The movements founder, Thomas Cole, was very much against Jacksonian Democracy, Manifest Destiny, and threats to develop America's untamed wild side.
Wow! Thank you so much for that answer. I see now that the piece is more about the landscape than the societal structure surrounding it.