Can't help you out with the perfect production.
I just checked the McBride DVD and I do it the same as Jeff shows it in the movie about this production. Only thing I can think of is maybe you put too much pressure on the cards while holding them. The more tension there is on the cards, the faster they will spring out of your grip, especially when the cards are really smooth.
I'm perfect producing cards right now too see if I can give some more help ...

wait, just found something I do different than Jeff in the video. The grip Jeff uses for the perfect production has the cards clipped between the palm and the middle finger, leaving the index finger and thumb free for the production and the other fingers don't tough the cards at all. The way I hold the cards for perfect productions use the ring finger also to hold the cards in place.
There are 2 reasons for me to change the grip a bit:
1. When using smooth cards they slip away sometimes when using too much or too little pressure in the grip. The ring finger prevents that.
2. I also use the ring finger to pull the cards back a bit. Sometimes when using only the middle finger to grip the cards I thought I could see the corners at the other end of the cards when practicing in front of a mirror. By pulling the cards back a bit more with the ring finger the cards are hiding further back into the palm, giving more cover of the hand.
Remember, the DVDs just show how a move works and how the teacher, in this case Jeff McBride, does the move. This does not mean it is how you must do the move. You can always adjust some things to make it work for you.
I learned all the productions from these DVDs too. I think they are excellent if you want to learn manipulations with cards. I can't compare it to other DVDs that show you the same material because I’ve never seen others. What I do know is that I once saw a promotional video for DVDs like the McBride series. During the promotion video I saw several card flashes, I thought the back palm productions were of beginner skill level. And I don't think I’m so skilful at all, but the promo video was just bad.
You can see the skill of a performer when he makes the pivot move. Jeff does it with a small motion of the hand. Then there is no room for mistakes while making the pivot move, anything wrong in your timing and the cards will flash. Sometimes you see a performer make the pivot move with a wide circle motion of the entire arm. While doing this your hand disappears behind the body for a moment. That is the moment these performers make the pivot move. Any screw-up will be hidden by your body. That is just the way the pivot move was made in that promo video I mentioned. The DVDs said: 'learn from the pro'. I thought: 'learn from someone who thinks he is a pro'.