Are you trying to embed a Juicebox gallery in a theme's header?
If so (and you know the gallery id you wish to display), you should be able to use the following code in your theme's 'header.php' file.
<?php
$JB = new Juicebox();
echo $JB -> shortcode_handler( array( 'gallery_id '=> '2' ) );
?>
... changing the '2' above to the gallery id of your choice.
Alternatively, the following should also work:
<?php
echo do_shortcode('[juicebox gallery_id="2"]');
?>
As you have discovered, the gallery's dimensions are tied to the gallery (being stored in the gallery's XML file) and a single gallery cannot be displayed twice with different dimensions each time. In fact, the same gallery should not be displayed twice on the same page because both galleries will create divs with identical names to be embedded into.
I would recommend creating a separate gallery for your theme and, if necessary, duplicating the gallery (with different dimensions) for use elsewhere.
The problem with your original code seems to be the extraction of the gallery id from your custom field as entering the code above (with the hardcoded gallery ids) seems to work fine. However, I would need to know more about the custom field you are using to help with the extraction process.
What is output if you echo $juicebox after defining it on this line:
$juicebox = get_post_meta( $post->ID, 'slideshow_embed', true);
For your subsequent code to work, the output would have to be something like: [juicebox gallery_id="2"]