I will try out your changes later in the day...

Meanwhile,

> I don't know what "pre-order" means. What about
> `org-flat-forward-element' 

By, flat or linear you really mean a serialized (or stringified) version
of parse-tree.  i.e., An Org buffer is really a serialized
representation of the parse tree.

> or simply (but misleading) `org-forward-paragraph'?

http://en.wikipedia.org/wiki/Pre-order_traversal

Even pre-order could be misleading.  

`org-forward-paragraph' is much better.  As long as the docstring or
comments mention that Org's notion of paragraph is much more nuanced or
richer than a text-mode's notion of paragraph.  

I insist on this, only because description (even if exhaustive) could be
misleading and restrictive.  But an Imagery (or a mental model) is
usually richer and generative.

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