I've read that A/B testing and MVT are best for testing smaller scale changes (i.e. button color, headline copy, etc), but are they also suitable for testing two (or more) very different designs? What's the best practice in a situation like that?
AB testing is perfect for a situation in which you can relate the difference in responses to the thing that is different between the two versions.
With two very different versions you can only gauge an overall response but not attribute a better or worse response down to a particular detail, and that makes it harder to put forward a reasoned argument for ongoing design. You don't know which features should be kept or should consider removing at a later date for example.
So you need to ask yourself:
A good exercise is to walk through what will happen if your testing shows A to be the preferred version - and then do the same if B were to be preferred. Also consider what if there were no preference. This will help you determine what is important and to perhaps reconsider how your testing is done