I am pretty qualified to give you good advice. I have a MS in Computer Science and I am currently a designer at a top of the line AAA studio. It's generally hard to go straight into design and honestly I am glad to have had a variety of programming jobs.
The key to making the transition to design is to always be improving your design skills. Listen to game design podcast, read game design books and most importantly, design games. In my humble opinion, having a MS in CS and a decent portfolio of games you created is 1,000 times better then any "design degree" or video game degree.
I've darted in and out of the industry a few times, do not let that discourage you.
Think about it like this, if you keep making games on your own, you'll eventually get good enough that you won't need a studio to work for because you'll be able to support yourself off your own creations.