Sorry for the delay! Though it's not an overview of the poetic tradition as a whole, you may find Kevin O'Rourke's Book of Korean Shijo [sic] of interest. Sijo is a very different kind of thing from Paridegi, but it comes to mind because of your Kokinshu translation project.
Quite aside from the Jimoondang repetition issue upthread, I have learned to steer clear of Peter H. Lee when there are other options, partly because he's had such a big footprint upon the English-language part of the field and partly because I've read enough of his articles (half a dozen?) to be wary of his scholarly rigor. (When you are sort of the grandfather of a discipline in the U.S., you get away with stuff, even if you're capable of doing more than you have been.) Anyway, there is a Lee-edited anthology of poetry more broadly conceived, published by Columbia UP; here's a review of it.
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Quite aside from the Jimoondang repetition issue upthread, I have learned to steer clear of Peter H. Lee when there are other options, partly because he's had such a big footprint upon the English-language part of the field and partly because I've read enough of his articles (half a dozen?) to be wary of his scholarly rigor. (When you are sort of the grandfather of a discipline in the U.S., you get away with stuff, even if you're capable of doing more than you have been.) Anyway, there is a Lee-edited anthology of poetry more broadly conceived, published by Columbia UP; here's a review of it.