If using WP-SimpleViewer (the dedicated SimpleViewer plugin for WordPress), instructions for upgrading the plugin to SimpleViewer-Pro can be found here.
Once the 'svcore' folder has been replaced, the plugin will have no option but to use the Pro files and the SimpleViewer branding will be removed.
If you have any doubt as to whether or not the Standard 'svcore' folder on your web server is being overwritten, try deleting it from your web server first before uploading the Pro version in its place.
Also, after making the change, you may need to clear your browser's cache before reloading the gallery to ensure that your browser does not hang onto and use older versions of your gallery files.

If you want to embed a gallery created by svBuilder-Pro into a WordPress page or post:
(1) Upload the complete gallery folder (not just the contents) to your web server. It does not matter where you upload the folder to as long as you know where it is.
(2) Use the baseURL method of embedding as documented here. When entering the embedding code into the page or post, make sure that the two paths within the embedding code (the path to the 'simpleviewer.js' file and the baseURL itself) are correct and that the method of entry is 'Text' rather than 'Visual'.

If you continue to experience difficulties, please post the URL to your gallery so that I can take a look.

There are two problems with your gallery's embedding code:

(1)

<script type="text/javascript" src="http://www.katewatson.org/gallery/Zambia Gallery/svcore/js/simpleviewer.js">

Your gallery's 'simpleviewer.js' file is not located at that location on your web server.

(2) The baseURL should point towards the gallery folder (not a file within the gallery folder).

For example, if your gallery folder is named 'Zambia Gallery' and you have uploaded the complete gallery folder (not just the contents) to the 'gallery' directory on your web server, then the following embedding code will work:

<!--START SIMPLEVIEWER EMBED.-->
<script type="text/javascript" src="http://www.katewatson.org/gallery/Zambia Gallery/svcore/js/simpleviewer.js"></script>
<script type="text/javascript">
var flashvars = {};
flashvars.baseURL = "http://www.katewatson.org/gallery/Zambia Gallery/";
simpleviewer.ready(function () {
simpleviewer.load("sv-container", "100%", "100%", "222222", true, flashvars);
});
</script>
<div id="sv-container"></div>
<!-- END SIMPLEVIEWER EMBED -->

Thank you for providing this additional information.
Knowing that your gallery folder is inside the 'wp-content' folder, the following embedding code should work:

<!--START SIMPLEVIEWER EMBED.-->
<script type="text/javascript" src="http://www.katewatson.org/wp-content/gallery/Zambia Gallery/svcore/js/simpleviewer.js"></script>
<script type="text/javascript">
var flashvars = {};
flashvars.baseURL = "http://www.katewatson.org/wp-content/gallery/Zambia Gallery/";
simpleviewer.ready(function () {
simpleviewer.load("sv-container", "100%", "100%", "222222", true, flashvars);
});
</script>
<div id="sv-container"></div>
<!-- END SIMPLEVIEWER EMBED -->

As you are using WordPress, you might like to consider using WP-SimpleViewer, the dedicated SimpleViewer plugin for WordPress which would allow you to create galleries within the WordPress Dashboard without the need to manually upload files and insert embedding code.

The code I posted should work fine.
Make sure that you clear your browser's cache to ensure that your browser is not hanging onto and using older versions of your gallery files.
Please post the URL to your web page so that I can take a further look. At present, your link above displays a 'You do not have permission to preview drafts.' message.

I would still recommend that you take a look at WP-SimpleViewer which would simplify the process of creating and embedding SimpleViewer galleries in WordPress pages and posts.

Your www.katewatson.org subdomain redirects to katewatson.org but your embedding code uses absolute URLs with the www.katewatson.org subdomain (which is not the same domain that the user's browser will be displaying after the redirection).
Please see this FAQ which deals with loading images from a different domain/subdomain:
When loading images from a different domain, the images don't load or I see a 'Security Sandbox Violation' error. How do I fix this?
The solution, in your case, would be to simply change the URLs in your gallery's embedding code to point to the katewatson.org domain.

Also, with regard to your gallery's height, try setting the height to be an absolute pixel value rather than a percentage.

Try the following embedding code:

<!--START SIMPLEVIEWER EMBED.-->
<script type="text/javascript" src="http://katewatson.org/wp-content/gallery/Zambia Gallery/svcore/js/simpleviewer.js"></script><br />
<script type="text/javascript">
var flashvars = {};
flashvars.baseURL = "http://katewatson.org/wp-content/gallery/Zambia Gallery/";
simpleviewer.ready(function () {
simpleviewer.load("sv-container", "100%", "600", "222222", true, flashvars);
});
</script></p>
<div id="sv-container"></div>
<!-- END SIMPLEVIEWER EMBED -->

Hi,

Also, as I will be embedding various galleries, can you please highlight the parts of the code that I will have to edit for each specific gallery (which I will install in the same location) page.

RT SIMPLEVIEWER EMBED.-->
<script type="text/javascript" src="http://katewatson.org/wp-content/gallery/Zambia Gallery/svcore/js/simpleviewer.js"></script><br />
<script type="text/javascript">
var flashvars = {};
flashvars.baseURL = "http://katewatson.org/wp-content/gallery/Zambia Gallery/";
simpleviewer.ready(function () {
simpleviewer.load("sv-container", "100%", "600", "222222", true, flashvars);
});
</script></p>
<div id="sv-container"></div>
<!-- END SIMPLEVIEWER EMBED -->

Thanks