Also, the time of the future is important as for the very near future, then would they be adjectives or verbs? (Putting on my coat- I'm going to meet my father at the station. Is this an intention pure and simple?)
What about the differences in the following:
1. Putting on my coat, I'm going to meet my father.
2. Putting on my coat, I shall meet my father.
3. Putting on my coat, I shall go to meet my father.
4. Putting on my coat, I am proceeding to meet my father.
I think (1) and (2) are closer in meaning. The futurity conveyed in (3) is not really the message in (1). As you pointed out, the imminence of the action should be a key factor as to the tense. The "meeting" is more imminent in both (1) and (2) compared to (3).
In my humble opinion, only the first sentence makes sense. In the first sentence, Putting on my coat is an adverbial phrase modifying the rest of the sentence. In the other sentences, it doesn't modify anything, having no genuine connection to the rest of the sentence. The first sentence could be restated as I am putting on my coat, and then I am heading out the door to meet my father. In the other sentences you are talking about two separate actions that are totally unconnected in every way.