After completing the quest "The Finger of Suspicion, I was given the quest "I Put a Spell on You" by Volpes Inculta. Now, I checked up on it, and found out that this quest can be done for either the Legion or the NCR. My question: how do I transition from a Legion approach (since I got the quest from the Legion) into an NCR completion?

My assumption is you cant.

The reason being, once you accept the quest from one side you cant go back and get said quest from the other.

Example if you talk to the powder ganger in goodsprings and agree to help him take over and then change your mind and talk to the crimson guy in the gas station he wont give you the quest saying you already got frindly with the gangers.