What you are looking to achieve could probably be achieved quite easily without the need to pass any image ids as parameters or use iframes (although it would need to be set up manually and could not be done with the existing WP-Juicebox plugin which is designed to embed Juicebox galleries directly into WordPress pages or posts).
You could create your galleries using JuiceboxBuilder-Pro (on your computer).
Upload the complete gallery folders (not just the contents) to your web server. It does not matter where you upload them to as long as you know where they are.
Just insert image links in your WordPress pages or posts to point to each gallery's 'index.html' file.
For example, if you uploaded a complete gallery folder named 'gallery1' to the root directory of your web server, then you could use an image link such as the following.
<a href="/gallery1/index.html"><img src="/images/thumbnail.jpg" width="80" height="60" alt="thumbnail" /></a>
(You would need to provide a suitable thumbnail image to use as a link.)
When the user clicks on a link, the browser would be redirected to the gallery's 'index.html' page which would display the gallery on a page of its own.
Your gallery could incorporate a Back Button to allow the user to return to the original WordPress page or post containing the link.
... there seem to be some issues loading Juicebox into an iFrame. There seems to be some flickering during animations, at least here with my Chrome brower.
This is a known issue which has already been addressed and will be fixed in the next version of Juicebox. However, just fior the record, there are other limitations of using an iframe which are documented in the 'Using an iframe' support section here.
I hope this helps.