I want a script which would just paste text from current clipboard and align it in the text frame. But I only figured out how to paste, and align it horizontally. How to do it vertically? So the text fits right in the center of the text frame. Here what I have done so far:
app.paste();
app.selection[0].parentStory.justification = Justification.CENTER_ALIGN;
Vertical justification is a text frame property so you'll need to find the frames corresponding to the story. Here's a snippet that picks up where yours ends.