This morning I tried to upload (publish) our project to the webserver, only to realize the SiteSpinner doesn't automatically pull all files into the upload. Also there seems to be no control over what files upload.

I had to manually upload quite a few things...

I propose that you give the customer more control over this process, since they'll be going back and using another ftp program anyway just to get the rest of everything uploaded.

You can upload all external files using Foreign Object Editor. The only thing is that some of the external files should be placed in specific folders but even that can be done. In some cases that is easier done with independent FTP Client.