I didn't know this was a thing, but apparently this is what you're looking for (although they don't all start with higgledy piggledy):
Double dactyl - Wikipedia
The named example, from the article--
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An example by John Hollander:
Higgledy piggledy,
Benjamin Harrison,
Twenty-third president
Was, and, as such,
Served between Clevelands and
Save for this trivial
Idiosyncrasy,
Didn't do much.
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And an explanatory one--
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A self-referential example by Roger L. Robison:
Long-short-short, long-short-short
Dactyls in dimeter,
Verse form with choriambs
(Masculine rhyme):
One sentence (two stanzas)
Hexasyllabically
Challenges poets who
Don't have the time.
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