It is interesting how one’s “Sprachgefühl” differs from one person to the next.
I wouldn’t say the “am”-construction is an “ugly mistake”. In fact, it is very commonly heard throughout Germany - at least western Germany, according to the link below, and also in Berlin where I live. The article even says: Laut Duden wird sie inzwischen „teilweise schon als standardsprachlich angesehen“ (it is partly considered standard language).
am-Progressiv – Wikipedia
As for the other forms, all express an ongoing action, as the name “Progressiv” implies (so not “about to”, but rather “in the middle of”):
- ich bin am Essen
- ich bin beim Essen
- ich esse gerade
- ich bin dabei, etwas zu essen
However, to me there are slight semantic differences.
I think “ich bin am Essen” and “ich esse gerade” are equivalent in meaning. They mean “I’m eating right now”, i.e. it is just about the action itself.
“Ich bin beim Essen” feels a little different, because it turns “das Essen” into more than just the action. It is an event that’s happening right now, like one of the meals of the day. Dinner is happening right now, and I’m participating. Of course it doesn’t have to be dinner, it can also be just you and your snack, but you make your own little ceremony out of it.
Maybe that’s why the “am”-construction is so popular. You don’t always want to make it sound like a ceremony.
Now, the last one is also different, because to me “ich bin dabei, zu essen” sounds kind of incomplete. It needs an object, something that the action is done to.
All of MRgK’s examples had an object: “es”, “einen Spaziergang”.
I’s hard to explain. I think it’s about completing something and reaching a goal. A verb alone is just an action, but if there’s an object involved, you have an “objective” you want to reach. And if you’re “dabei”, then you’re “at it” or “on it”, i.e. actively pursuing the goal.
So MRgK’s example:
Hast du das Buch schon gelesen? - Have you read the book already? (it’s like a TODO item)
Nein, (aber) ich bin gerade dabei (, es zu lesen). - No, but I’m reading it now / I’m on it. (You’re right I wanted do do this, and I’ve been procrastinating, but now I’m working my way through it)
As you see “Ich bin dabei” can be enough if the goal has been mentioned before.
I’m sorry this has become a rather long post.