Higgledy piggledy and tiddley quiddley are often used in a type of comic verse known as double dactyl. A dactyl is a poetic measure consisting of one long and two short syllables. Like "higgledy". So "higgledy piggledy" is a double dactyl."
Now, with that out of the way, let's try a couple. (Both make use of "incomprehensible" which has the advantage of being a double dactyl all by itself.)
Higgledy-Piggledy, Young Dr. Frankenstein. thought he was able to cook up a man. baking and broiling and incomprehensible things to invent such a Frankenstein plan.
or
Tiddley quiddley
Edward M. Kennedy
quite unaccountably
drove in a stream.
Please of amnesia,
incomprehensible,
probably shattered
political dream.