grammaticality - 'starting cleaning' vs 'starting to clean'

In an answer to this ELL question, one of our users provided this example sentence, claiming it was grammatical:

He sighed starting cleaning the floor.

That sentence seems to clash in my native ear. I suggested that it wasn't good grammar, and that (assuming I'm understanding the gist of the sentence) it should be restructure to something like:

He sighed, and started to clean the floor.

or

He sighed and started cleaning the floor.

In a comment, though, the user who wrote the sentence stuck by the claim that the original example sentence doesn't violate any grammatical rules.

Rather than start a protracted debate under the comments over there, I figured I would simply ask about the matter here in a new question.

Is this sentence acceptible from a purely grammatical standpoint? Is it colloquial?

I did find some sentences online that used the "starting cleaning" word pair, but they weren't really using them as consecutive verbs. For example:

A broom, mop, sponges, dish soap, hand soap, paper towels, and all-purpose cleaner should serve well as a starting cleaning package.

In this case, both starting and cleaning modify package adjectively, so, even though that sentence uses the two words, it's meaning and grammatical structure are quite different.

Should I retract my comment? Or keeping sticking [sic] to my guns?

Answer

Grammatical? —

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  Conventional orthography, whether mechanical or rhetorical, demands a comma after sighed. Is punctuation a matter of grammar? I dunno; but it's certainly a factor in intelligibility.

  
  
  


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  Starting cleaning is syntactically acceptable—start undoubtedly licenses gerund complements. But I think it would grate on most native hearers, because it violates the horror aequi principle. Is that a matter of grammar? I dunno; but it's certainly a factor in acceptability.

  
  

  ADDED following pointers from F.E., DamkerngT and Araucaria: Geoffrey Pullum and Arnold Zwicky (names to conjure with!), 'Gerund participles and head-complement inflection conditions', in Collins and Lee, The Clause in English: In honor of Rodney Huddleston, 1999, find an explicitly syntactic constraint: "It is not acceptable in most varieties of modern English for a complement (as opposed to an object) marked with gerund participle inflection to be adjacent to its matrix-clause verb when that verb is likewise in gerund participle form."

  
  

Just as there are lots of technically legal practices which honorable merchants will not perpetrate on their customers, there are lots of technically grammatical constructions which good writers will not perpetrate on their readers.