There's a contemporary music technique called a twelve tone row, which could be its own whole longpost, but the quick version is: every note in the twelve-tone chromatic scale must be used before returning to any already-used notes, and lots of people like to add constraints to the construction and use of twelve tone rows after that.
I think there's something interesting and overlapping with twelve tone rows and alphabet poems. In both cases, all members of a set (either chromatic notes or letters of an alphabet) must be used before any returns to already-used set members.
It makes me wonder whether, rather than trying to only do alphabet poems in alphabetical order, or rather than only using each letter once in the whole poem, could there be interesting poems made from using each letter once per group but never using any that are directly next to each other alphabetically? Could this be sustained for many groups?
Here's a tool for shuffling the alphabet if you're interested in trying it out: