I also switched a (pretty customized) MT weblog from one host to another. After thinking about it, I decided it would probably be easiest to just do a fresh installation of Movabletype at the new domain, copy my customized templates over the defaults, copy my customized stylesheet over the default, check my other misc little tweeks and then import the data from the old blog to the new one.
Some might argue that this was a convoluted way of doing it but, it took almost no time, made me review what I’d done previously, and worked perfectly the first time.
Importing blog data is pretty easy, but read the instructions in the MT manual first. You need to create an import directory and you need to export the data from your current blog. IE doesn’t export properly, so use mozilla or netscape.