As a hosting industry expert and I say expert because I have been hosting for 16 years, my opinion is that you should get an account at a registrar and keep the domains separate from whatever hosting service you use. Always keep your domains separate from hosting just in case of situations like this and also gives you more control over what you need to do. Usually, if you have your domains with your hosting provider, you have less flexibility to change things, such as DS redirection etc.
If you have more questions, feel free to PM me.