I'm afraid your prior assumption is incorrect. These are not "dangling participles". These are just ordinary participles.
Many participles, like those in (1-4), are formed from reducing relative clauses, like those in (1'-2'). They are not ungrammatical, and the participles in (1-2) are not "dangling". (3-4) are similar in structure, and there's nothing grammatically wrong with them, either; nor do they "dangle".
The construction that's condemned as a "dangling participle" has to be a participle that lacks a subject. Most participles do, but it's easy to see what the subjects would be in (1-4), because the participles come right after them. That's not "dangling" -- that's being properly placed.
Besides being subjectless, a "dangling participle" has to be placed in the sentence in a way that points to an incorrect subject. Since subjectless participle phrases often are adverbial in meaning, they can be moved around, by various rules, viz:
- Three cats were sitting on a fence.
- Sitting on a fence were three cats.
- There were three cats sitting on a fence.
- Sitting on a fence there were three cats.
But this can isolate a participle from its subject, especially if the sentence is complex:
- My grandmother saw three cats sitting on a fence.
- [Sitting on a fence] my grandmother saw three cats.
These last two sentences don't mean the same thing, and the bracketed part is an example of a real "dangling participle". The "dangle" part of the metaphor refers to the unfilled subject slot of the participle, which gets attached to the wrong noun, like a dangling chain caught on an obstruction.
As one can see from the example, dangling participles are the basis of many jokes.