Moving Blog and Domain at Same Time

Hi, I’d like to change hosts. Let’s say, for example, that I have me.com at Media Temple, and I’d like to move the domain me.com, and the wordpress content, over to BlueHost.

It’s easy to Export the blog from the existing site.
It’s easy to move me.com from pointing at Host A to pointing at Host B.

But then when I try to Import the content to, for example, BlueHost, how can it download the old content if I’ve taken me.com off MediaTemple?

I guess I could do the Import for the posts and FTP the files in place, but then all the media will be unattached, right?

Thanks!