Not being an English native, I don't see the exact nuance between "I'm in the process of eating" and "I'm eating". I still think that "I'm eating" is "je suis en train de manger". It's also the way we're taught it in French schools. Also, we never learnt "in the process" for "en train" either. I'm noy saying that our schools are always right though
. But in my own experience in reading English, I still think that "en train" is appropriate. Maybe I'm biased.