The timeout thing is double edged, cause it comes from both us (i.e. where you’re moving TO) and your old host. It has to download all the media on the fly.
One thing to keep in mind, if you break up your imports into smaller chunks, it tends to work better. Or you can keep re-importing, and WP should be smart enough to know “Oh I have that post on the smurfs already, let’s move on.”