Juicebox and SimpleViewer run on different platforms (Flash vs HTML) and have different sets of configuration options so it would be difficult to exactly replicate a SimpleViewer gallery using Juicebox.
However, the following notes might help you to get close.

This is possible. Each thumbnail in a Juicebox gallery is assigned a unique URL so you could create your own thumbnails and point towards then using the thumbURL entries in the gallery's XML file.

Juicebox-Pro configuration options such as imageScaleMode and imagePadding (and rearranging other gallery elements) might help you achieve a larger main image in your gallery.

You can position the thumbnails in a 3 x 3 grid to the left of the main image in Juicebox-Pro (though not in Juicebox-Lite, the free version) by setting thumbsPosition="LEFT", maxThumbColumns="3" and maxThumbRows="3" in your gallery's XML file.
Here is a demo Juicebox-Pro gallery which closely resembles a SimpleViewer gallery.
Other demo galleries which demonstrate what can be done with Juicebox-Lite and Juicebox-Pro can be found here.

Many WordPress themes use a central column to contain the content with large borders to the left and right sides.
With the usable width of the page reduced as it often is, the default Juicebox layout (thumbnails below the main image) is likely to be the optimal layout for most WordPress users. If you were to position the thumbnails to the left of the main image, there may be little space remaining for the main image to be displayed and it might appear very small. If doing so, I would recommend that you reduce the size of your WordPress theme's borders to accommodate such a Juicebox layout.

By default, a Juicebox gallery's XML file will be named 'config.xml' and will be inside the gallery folder alongside the 'jbcore' folder.
However, if using WP-Juicebox, the gallery's XML file is generated dynamically using PHP at the time the gallery is displayed so it cannot easily be modified manually.

This sample gallery uses Juicebox-Pro configuration options so you would need to first upgrade WP-Juicebox from Juicebox-Lite (which it comes bundled with) to Juicebox-Pro by following the instructions here. You would then need to enter the following configuration options into the 'Pro Options' text area:

thumbsPosition="LEFT",
maxThumbColumns="3"
maxThumbRows="3"

If you want to embed a gallery into a WordPress post which contains custom thumbnails which are not simply small versions of the main images, then you could:
(1) Create a Juicebox gallery with Juicebox-Lite
(2) Swap the thumbnail images in the 'thumbs' folder with your own custom thumbnails (and edit the thumbURL entries in the 'config.xml' file if necessary)
(3) Upload your complete gallery folder (not just the contents) to your web server. It does not matter where on your web server you upload the gallery folder to as long as you know where it is.
(4) Embed the gallery in your WordPress post using the baseUrl embedding code found here, making sure that the two paths within the code (the path to the 'juicebox.js' file and the baseUrl itself) are correct. Also, when entering the embedding code into your WordPress post, make sure that the method of entry is 'Text' rather than 'Visual'.

It looks like there may be a conflict between the CSS of your current theme and the CSS of the gallery itself.
Try temporarily reverting to the default WordPress theme to see if this makes a difference.
If it does make a difference, then your current theme may use some generalized CSS rules which apply globally to certain HTML elements (rather than to specific instances of these elements through use of ids and classes) which the gallery inherits.
Check the CSS of your theme and try removing any generalized CSS that you can find.

This would be a CSS rule that is applied to all instances of a particular HTML element, such as a div.
For example, something like:

div {
    display: none;
}

... will apply to all divs on your web page (including those in your Juicebox gallery), whereas:

#sample {
    display: none;
}

... will apply only to the div with id="sample".
It sounds like your theme may be the root of the probem. Please let me know whet theme you used so that I can investigate further.

Your gallery currently used the following code:

backgroundColor: '#222222'

Change this to:

backgroundColor: 'rgba(0,0,0,0)'

The 4th parameter of the rgba expression (the alpha channel) is the opacity of the background (0 being transparent and 1 being opaque). If you use a 6-digit hexadecimal code rather than an rgba expression, the gallery's background will be opaque.
If using JuiceboxBuilder-Lite to create or edit your gallery, set the opacity of your gallery's background color to 0 on the 'Customize' tab.

Thank you for letting me know the theme you use.
I have installed and activated the theme and can now see the problem that you have described.
It looks as if the root of the problem lies with line 62 of the 'gridiculous/style.css' file:

*{-webkit-box-sizing:border-box;-moz-box-sizing:border-box;-ms-box-sizing:border-box;box-sizing:border-box;word-wrap:break-word}

Removing the line allows the Juicebox gallery to be displayed as it should be but I do not know what knock-on effects removing this line of code will have on the theme itself.