There isn't a whole lot I can say that you can't figure out with a few hours of messing around with the pressures involved, but here's what I've found helpful.
You don't have to slide the card out with your pinky, the original Kennedy deal (references listed below) involved using the middle finger from a very (imo) awkward grip. Jason's technique as I recall is a hybrid of the Kennedy center and a Jim Cooper idea.
Assuming you're right handed and the pack is in your left hand. Your thumb is going to apply downwards pressure to the top LEFT corner of the deck. This anchors the left side of the deck to your thumb crotch, you'll find that a gentle squeezing action of the bottom half will enable your left fingers, using upwards pressure on the RIGHT side of the deck, to slide out the bottom card of the top half. As soon as you get 'feel' that you've gained control of the center card, release pressure from your thumb and this will allow you to slide out a single card relatively easily.
This is what works for me. I think it's simply an issue of distinct opposing pressures from the downwards left and upwards right pressures on the deck. There's also a temporal element involved, so what it really boils down to is just lots and lots and lots of practice until you figure out what works for YOU.
I asked Jason the same question a few years ago and he mentioned that the problem of the sliding top half is something he was never completely able to get rid of. In my opinion, this isn't a problem in the original Kennedy deal. However, the original Kennedy deal is also significantly harder to do, although I would recommend that you learn it and understand it. It'll make Jason's technique make more sense and accelerate the learning process. I've listed the three places that it's been published below in chronological order. Revelation (2008) has the most comprehensive description. Also, if you haven't spent a significant amount of time on the bottom deal, I would recommend that you learn the bottom deal first.
Allan Kennedy Center Deal
1. Ross Bertram's "Methods and Magic of Ross Bertram"
2. David Ben article in Genii December 2001
3. Dai Vernon's Revelation (2008)
Hope this helps
Thanks a lot Ted!
The advice is really helpful, and I will for sure look into the sources provided.