This g3 rest script is an excellent embed option for Gallery 3.

The trick to getting this to work in the joomla framework was to switch from the provided combined javascript to the individual source scripts. Just switch to the commented out scripts already provided in the example page. The colorbox is still black due to my permissions.

the script also works externally from the public html directory.

Local file on L Rio.

The issue persists with the colorbox black or blank. The miscellaneous/furniture album has permissions set to full size view: everyone. the colorbox and swipe work in this instance.
The black or blank problem stems from the galleries have to be set to view full size at the g3 site.
My g3 structure and planning is set to have full size turned off for the public to allow printing for users.
The page on Flash your Web.
The topic on the Gallery 3 Forums