Kogachi Ryūichi made a short post on his blog back in 2013 containing an interesting observation about Shǐjì 史記, as in the modern title given the Han-era Records of the Grand Historian 太史公書. It seems that in Wang Li's reconstruction of Middle Chinese, 史記 is ʃǐə kǐə, making it a 畳韻 or "paired-rhyme disyllabic compound" (credit to Jingtao Sun [PDF] for this English term).

I don't know enough about rime tables to engage with the idea properly, although I will note that the Baxter and Sargent reconstruction looks less like a rhyme: MC sriX kiH < OC *s-rәʔ *C.k(r)ə(ʔ)-s. Still, the idea that the venerable-sounding title Shǐjì might have the same morphological motivation — meta-etymology? — as, say, "look book" is too good to ignore.