Thank you for your suggestions Tim and Torsten. It's great to have a list of possible solutions to test with my data set.
It sounds like reducing the degrees of freedom in my registration is a promising first step. And then I can play around with the other tricks Torsten suggested.
I agree that manually cropping the reference for each subregion image stack may work well. But, I am a little concerned because I do not have exact structures to use for cropping my reference. I will have to use my best guess and see if the accuracy of the mapping is good enough.