I did a search in GQ as I figured this one would’ve come up before but didn’t find anything. I was in an Army surplus store today and noticed the peacoats. I had one many years ago, but never heard how they got the name.
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It definitely pre-dates our Navy coming up with the term. In the American Weekly Mercury in 1721; “Cloathed with a double-breasted Pee-Jacket.” Probably from the Dutch, wouldn’t you know it 
pij-jakker.
Link to comments by Evan Morris, at his website The Word Detective (www.word-detective.com): Peacoat
He traces the “pea” back to “pee”, a rough cloth in England.
There ain’t much better than the Word Detective when it comes to tracking down word origins, IMHO.
Nothing to contribute, except that I like my peacoat! (Too bad it’s not cold enough down here so I can wear my Russian Navy ushanka with it!)