this is a very nice family of structures; perhaps you could use it to choose which previous line in a poem to rhyme with, or which previous day to reflect on
to avoid the collapse from transitive equality, I think rhyming would need to work in pairs, rather than in lines, something like AABBAACCAABBAADD... (giving an ostinato effect, similar to a ghazal?)
(...GCAABBCDEEFFDG... might be interesting to write with the quatrains displayed block inline but the longer-range rhymes just set as normal prose; it would be up to the reader to notice the maintenance of metre and rhyme in the nominally "prose" sections)