It shouldn't be doing that at all, even with the stock exhaust. You should upgrade for sure, but it sounds like You have some tuning/diag. to do. That said, if it's going to require re-jetting/pump-shot/timing-curve changes, do the exhaust first.
I'm taking it in this Friday for the post break-in adjustment and I'm hopeful that most of the problems will if not disappear at least fade. I'll have to wait for the big tune until I can get the new exhaust.
What's the current information regarding horsepower/torque differences between Y pipes, X pipes and H pipes?