It *sort of* works in that I get LaTeX table syntax wrapped with
\begin/end{threeparttable}, but then I caught that threeparttable is
actually a wrapper around tabular. Not sure how you can currently use
Org to specify two layered wrappers like that? Or you might need
someone to write an equivalent of #+begin/end_center for
threeparttable?

#+begin_threeparttable
table-generating-stuff
#+end_threeparttable

Even more complicate is that tabular ends, then a tablenotes
environment begins/ends, and only *then* does threeparttable end.