Are these garden path sentences grammatically correct?

Background

A garden path sentence is one that is exceptionally hard for the reader to parse. English is especially prone to this because it is an analytical language and so many words can be many different parts of speech. I read that as a person reads a sentence, he builds up a likely meaning for each word and a meaning for the whole sentence word by word, then if a "disambiguating word" appears that changes the meaning, he switches to the new meaning and continues. When the disambiguating word is far away from the ambiguous word, the sentence can be very difficult to understand.

The classic garden path sentence, as far as I am aware, is "The horse raced past the barn fell." The ambiguous word is raced and the disambiguating word is fell. For those who don't think this is a perfectly grammatical sentence, the meaning is the same as "The horse [that was] raced past the barn fell." Or perhaps more clearly using a different word, "The horse driven past the barn fell."

Before I ask my question, since these things are so cool (to me, anyway), here are a few more examples:

• The old man the boats.
• While Anna dressed the baby spit up on the bed.
• The man returned to his house was happy.
• Fat people eat accumulates.
• She told me a little white lie will come back to haunt me.
• We painted the wall with cracks.

The Question – My Own Garden Path Sentence

After enjoying these and many other garden path sentences I read about, I invented one of my own. Recently I told it to a friend, but he didn't really get my example garden path sentences (the horse, the old, and Anna) and argued that they and mine were not correct grammar. So I submit it to you for your analysis:

The men run through the arches screamed.

As explanation, the men were stabbed in the feet, possibly as a form of torture.

I swear I had several others I invented five to ten years ago, but I can't remember them. Perhaps I will invent some new ones.

Is that sentence correct grammar? As well as the others?

Feel free to edit my grammar. No comment necessary.

Here is how the example sentences are grammatical:

• The old man the boats.
  The old [people] [man/serve on] the boats

• While Anna dressed the baby spit up on the bed.
  While Anna [got] dressed, the baby spit up on the bed.

• The man returned to his house was happy.
  The man [who was returned to his house] was happy.

• Fat people eat accumulates.
  [The fat that people eat] accumulates

• She told me a little white lie will come back to haunt me.
  She told me [that] [a little white lie will come back to haunt me].

• We painted the wall with cracks.
  We painted the wall [that has] cracks.

One of your examples is punctuated idiosyncratically:

While Anna dressed the baby spit up on the bed.

I've always been taught and I've always taught that adverbial clauses starting a sentence need to be followed by a comma:

While Anna dressed, the baby spit up on the bed.

This isn't mere disambiguation. Rather, the comma grants that clause -- "While Anna dressed" -- its capacity to modify the verb in the independent clause "the baby spit up on the bed." It's the grammatical way of saying, When did the spitting happen, you ask? Well let me give you something to modify that verb. Omitting the comma signals that "While Anna..." will be a noun clause: "While Anna dressed the baby [...was when the doorbell rang]." In this one case, the reeling "garden path" feeling of realizing that the verb "spit" doesn't fit with the noun phrase in front of it is legitimate and caused not by the reader's hasty assumptions but by punctuation that is grammatically uncommon.

Your other examples, though, are wonderful, as they play on grammatically common patterns formed with unexpected combinations.

All the sentences are grammatically correct, including your own.

You could make the meaning clearer by adding punctuation, but this might spoil the fun. For example:

The men, run through the arches, screamed.

I think you are missing something very important here: you're not using any punctuation at all, and that can make a big difference. If you write "While Anna dressed the baby spit up on the bed." your sentence is confusing, but if you write "While Anna dressed, the baby spit up on the bed." with a comma after "dressed", then it becomes an easy to undestand and correct sentence. Punctuation is important for grammar, so, if you don't use any punctuation in your sentences, they're gramatically wrong. There are no difficult to understand sentences, there are only wrongly written sentences.