Katie,
I had gotten a backup file of my Tumblr in XML previously but can no longer say how. I looked all over last night trying to find how I had done it (from the Tumblr site) but cannot.
Using that XML backup I used the WordPress importer under Import in my dashboard and it worked beautifully.
Hopefully the above solution works for you. If it is that simple it seems either the plugin or the API site could mention it though.
Mark