This is what worked TO AN EXTENT (no page breaks in table):

----------------
  (At top of org file:)
#+ATTR_LaTeX: longtable align=l|lp{3cm}r|l
#+LATEX_HEADER: \usepackage{pdflscape}

 #+LaTeX: \begin{center} \begin{landscape}
#+LaTeX: {}\begin{sidewaystable}\footnotesize

[ORG TABLE HERE]

#+LaTeX:\end{landscape} \end{center}
#+LaTeX: \end{sidewaystable}

-----------------

No such thing as breaking across the page happened.  Neither was I able to
use longtable to do so.

Alan