What I was looking for, functionally, was ...
- the ability to create a new menu link to an existing page
- retain my pretty-urls
- have the url display the new menu path
- have the breadcrumb trail show the new menu path to the page
This is exactly what page-copier provides.
So, now I can have a menu system which lists, for example, businesses by business type...
business-advertising/trades-people/electrical-services/toms-electrical-services/
...and business by suburb...
suburb-index/sydney/electrical-services/toms-electrical-services
...and have the menus point to the same page.
If you are familiar with Drupal, it is similar to their taxonomy.
My suggestion of changing the page-id in index.php doesn't provide the same features as page-copier.