Drupal - How can I move taxonomy terms to a different vocabulary and update term reference fields?

This tutorial suggests doing it via directly performing SQL queries to change the associated vocabularies for the terms in question.

The term reference fields should be by term ID. The term ID should not be changing, only the vocabulary value associated with the term entity.

Did you try to move term to new vocabulary with Taxonomy Manager (with double tree)? Term references are to TID , when you move terms to another vocabulary TIDs are saved and are the same. So i think that this will work