ianjones spake thus:

... I think the best and cleanest install would be to use (if it
exists) a screw that is threaded on both ends. With a couple pilot
holes I could screw into the extension and then twist the whole unit
onto the existing post.

Such things do exist; they're called dowel screws, basically a
double-headed wood screw.

But keep in mind that this would be the weakest possible way to do it,
since screws don't hold well in end grain, which is where they'd go in
this case. Dowels would be better, but, as you point out, a pain in the
butt if you have 45 posts to extend. Plus they'd have to go pretty deep
into both ends.


--
Save the Planet
Kill Yourself

- motto of the Church of Euthanasia (http://www.churchofeuthanasia.org/)