Unsolvable Views Problem -- Need Help

OK...

Should I just "add" this snippet to that function instead of creating another one

YES. you cannot re-define the same function twice, so you need to integrate the snippet into your existing _phptemplate_varialbes function

However, the function you provided in template.php would cover all instances of the node url -- is that right?

Yes and No. Your solution of printing the url override directly in node.tpl.php will work just fine - but it will do it for all node types, not just events, so now all nodes will link to "/event/[nid]/overview".
What my code (attempts to) do is fix the $node_url variable for only node types you want. I have set it up to do 'event' node types (please ensure your node type really is named 'event' - that's the machine name), but it could also do, say, a 'news' type, substituting the url to "/news/[nid]/overview".

However - you are right - there IS a bug in my code. The variables that are sent to the tpl are stored in the $vars array - so here's a (hopefully) fixed version:

<?php
function _phptemplate_variables($hook, $vars = array()) {
  switch ($hook) {
    case 'page':
       // stuff to set up variables for page.tpl.php
    case 'node':
       $node = $vars['node'];
       // stuff to set up variables for node.tpl.php

       // This snippet will override the URL for a node...
       //   from "node/[nid]" to "[node-type]/[nid]/overview"
       $override_types = array('event');  // add more node types here if you like
       if (in_array($node->type, $override_types)) {
         $node->path = '/' . $node->type . '/' . $node->nid . '/overview';
         $vars['node_url'] = $node->path;
       }
    break;
  }
  return $vars;
}

Sorry about that - I tested this version quickly and it seems to work.

but that doesn't get me all the way because I have to have that same node url changed in every instance

Hmmmm. View tables and lists are created by a function in Views - I'd have to look at that code to see how to override the default behaviour...
Also - check the "page" title link when a node is shown in Full view - Drupal does some funky stuff with the title in that case (thus the if ($page==0) bit around the title handling in node.tpl.php)

Question: I need to be able to test whether or not this function that you've given me is actually being processed in template.php.

What you tried there won't work (for the same reasons the code I gave you didn't ;-) If you want to see if the script is being executed, put the following statement just above the break;:
print 'Processing Node type: ' . $node->type . ' URL=' . $node->path;

If you are curious about what your node looks like after processing, put this just before the break;:
print '<pre>'; print_r($node); print '</pre>';
But only look at a page with one node or teaser, or it will generate too much output...

Anyhow - for the time being, get the script working and I'll see if I can pull out some time today to look at overriding the List and Table views...