It is actually rather difficult to construct a context for "estuve comiendo" that makes sense. I was having trouble coming up with something, so I googled it with quotes. Here are a couple I came across. They work, but they sure aren't commonly found!
Aquel éxtasis duró todo el tiempo que yo estuve comiendo. (That ecstasy lasted the entire time I was eating.)
(I guess there was something special about that particular meal.)
Últimamente anduve estresada y a las corridas y estuve comiendo muy mal, mucha comida chatarra y azúcar. (Lately I was stressed and always rushing, and I was eating badly, with a lot of fast food and sugar.)
In both cases, we see that there was a period in which eating occurred, but that period had a clear ending, i.e. it is not going on any longer.