Success!
It certainly looks like my problem revolved around not properly disposing of objects as they were created. Since I was iterating through thousands of objects, they were really piling up.
In the end, I needed to make sure I performed the .Dispose() on my Regions, Planes, and xPlode.Items (lines, ellipses, and circles) as soon as I was finished with them.
Thanks to all took a look and/or offered suggestions.
