How much data do you currently have at MT? If it is under 2GB you should be able to use their backup function to generate a tar.gz of all of your websites. Then, you should download this file and upload your data to your new FTP(s) at KH.
Then, you can use phpmyadmin to restore any MySQL databases, or do it via shell (google for the command).
Recreate any e-mail accounts, make sure your sub domains are in-tact, etc. It shouldn't be too hard to get this done, would take the day at most depending on how much data you've got, probably only a few hrs.