I have always held the pick between my thumb and my index and middle finger.  I felt like it was better because the pick would spin less, or I wouldn’t drop it as much.  My grip when strumming was more relaxed.  Now, I fear that maybe I should make the effort to learn the grip you’re describing.  When playing around with it today, I can flat pick better.  Who knew?  Not me.  But strumming is kind of clunky.  I hate the idea of starting over.  But, maybe it will be worth it in the end.  Advice, feedback?