With JuiceboxBuilder-Pro and the Juicvebox-Pro plugin for Lightroom, you are able to create as many individual galleries as you like. However, as you are aware, there is no automated method for linking galleries together.
If you are having trouble trying to replicate the online demo, then maybe the single-page solution that I created for this forum post will help.
Otherwise, if you have a need for a more complex and feature-rich solution, you might like to look into another of our products: Showkase.
Showkase is a PHP web application (installed on your web server rather than your computer) which allows you to create a complete portfolio web site (integrating multiple galleries) online.
Showkase has full support for Juicebox-Pro and the galleries can be created within the application itself in a web browser interface (or created with JuiceboxBuilder or the Lightroom plugin and then imported via Showkase's 'Site -> Import' functionality).
You can create Gallery Index pages and have as many galleries listed on each Gallery Index page as you wish.
Each gallery is represented by a thumbnail image with the gallery title displayed below and the gallery is opened when the user clicks on the image (just like your current website).
Demo Sites created with Showkase can be found here and a sample Gallery Index Page can be found here.
Showkase can also create non-gallery pages (About, Basic and Contact pages) where you can add information about yourself (or any other content you like).
All of this is done automatically within the Showkase interface without the need for any manual coding at all.
You can take a look around the Showkase interface by logging into the Live Demo Admin.
Showkase can be purchased as Showkase-Standard (which comes with Juicebox-Lite, the free version) or Showkase-Pro (which comes with Juicebox-Pro) from the Download Page.
The only difference between Showkase-Standard and Showkase-Pro is the bundled viewer (Juicebox-Lite vs Juicebox-Pro).
As you already have Juicebox-Pro, you could purchase Showkase-Standard (if you wanted to) and integrate your Juicebox-Pro files by following the 'Installing Juicebox-Pro' instructions here.
actually copied the code from that page and typed it into my test gallery index.html page ( that was empty).
If you want to persevere with the online demo, then rather than try to insert the demo code into your gallery's web page, it would be better to do it the other way around; use the demo page as a template and modify it as required. (The gallery's 'index.html' page is essentially just a plain web page with the gallery's embedding code and nothing else, so it would be better to use the demo page (rather than the gallery's 'index.html' page) as a starting point.)
If you get stuck, just upload your dysfunctional gallery online, post a link and I'll see if I can figure out why it's not working.
Having said all that, I hope that the single-page solution from my forum post (here) is a suitable solution for what you are looking to do.