Gosh. I'm not qualified to disagree with you there.
However, I feel like there are actually farrrrr too many commas, with almost every sentence including at least one. For me that doesn't seem to mix up sentence structures at all. I also feel that this:
We were rounding the southern coast of Africa, and while we were due to stop in the port of Durban in a few days for some much needed supplies, I found myself praying more than a few times for something to break the utter blandness of hardtack and beer, the monotony of looking out at the horizon and seeing the same thing day after day.
should not be all one sentence. For me, it's harder to follow this way and becomes monotonous.
At first, the lightning and rain proved to be a welcome change, a way to relax as I lay across my cot, listening to the music of nature that our Lord had seen fit to create with his Hands.
This as well. I can see how someone could say it creates more of a lulling effect, but I personally don't like it.
In this sentence:
With a growing panic, and not wishing to see my belongings strewn across the room, I seized my Holy Bible and my journal, and I wrapped them in cloth and crammed them in my jacket, as I blew out my lantern.
I feel like a parenthetical phrase would've helped to change up the structure in a new, different way. Also the comma after the word "jacket" feels like it shouldn't be there, as well as the second half of the sentence seeming tacked on when (in my personal opinion) should've been a sentence on its own.
Worried, and wishing to know what was happening, I hurried up to the top deck with all due expediency.
Here, the comma after "worried" isn't necessary, unless I'm incorrect there.
In summary, maybe it wasn't always particularly "wrong" per se, but it's definitely not a style I appreciate (and it comes off as sloppy and lazy to me). If it wasn't ever sentence I wouldn't have a problem, but it basically is.