Custom Taxonomy Permalinks Redirection

What is the best way to allow http://www.domain.com/newtype/newtax-term/post-name/ to load, without redirecting?

You have to add a custom rewrite rule to make this work. Otherwise WordPress doesn’t understand the newtax-term part of your permalink structure and redirects you to the URL which it does understand, which is %post_type%/%post_slug%.

If you want to understand how WordPress Rewrite API works, I would recommend you to read The Rewrite API: The Basics article. Spare no effort to learn it and you won’t have issues with it.