This is about as clearly written as I could ever hope a crypto writeup to be! So first off thanks for that! But I also agree with your comment, it really helps

This is about as clearly written as I could ever hope a crypto writeup to be! So first off thanks for that! But I also agree with your comment, it really helps to understand the "why" to know where this tool sits on the overall shelf. Or even just a bit more background on existing double DH constructs and specifically what problems this addresses and a use case where you choose this protocol specifically to gain some specific necessary property that you don't get otherwise with other DH constructs. The special padding during the hashing step seemed a bit odd, not sure why it was quite so many bytes? I would also love to see pseudo-code, some test vectors, and a sample hex encoded output of an exchange.