I finally managed to move my blog over to Wordpress with my new host. It just took a little BlogML export from SubText and a little XSLT to transform it over to the WXR format that Wordpress supports.
I did have one pain point though - Wordpress.com (the free hosted Wordpress version) allows for WXR imports. Assuming that a self-hosted Wordpress on DreamHost would be the same, I targeted WXR as my import format. Unfortunately, WXR isn't supported as an import format for the self-hosted Wordpress! :(
So in order to do the import, I had to import the WXR into a free account that I created on Wordpress.com and then export it into a format that was supported in the self-hosted Wordpress. A bit of a pain but nothing too bad.