Any advice in importing multiple email accounts?

You may wish to ask the users who are willing to do so if they could download any messages permanently that they don't need to keep on the server. This way the data is far smaller for the transfer. As for using Thunderbird or Outlook for the data, I don't know which is a better option for a massive download and transfer to another machine.

Also, if you were somehow able to get sudo su access to the machine (if the provider would be willing to give this to you), you could transfer these accounts using WHM > Transfers area at that point. We don't require direct root password, but we do require that the shell user can sudo to root level.