I did this--Dinan Stage III suspension on my Competition Pkg car. While it might seem pointless to order the Comp Pkg in the first place if you're planning on doing the Dinan suspension, the Comp Pkg does offer you the nice ZCP wheels and improved, more track-oriented programming of the EDC.
While the Dinan suspension will not offer any more of a lowering compared to the already-lowered Comp Pkg, it does offer a few key improvements: it includes camber plates to allow increased negative camber in the front, and it changes the bump stops so that despite the fact that the car sits lower than a standard M3, it actually offers MORE suspension travel. Both of these features are very helpful in a track setting in keeping the contact patches planted.
Now that I've completed my first full HPDE season with the car and am really getting into it, I've sometimes wondered if it would have been better for me to have ordered a non-ZCP, non-EDC car and just put on Moton coilovers or a JRZ setup, etc. But I must say, for my skill level (intermediate) the car does very well on the track with the Dinan setup and Nitto NT01s. And the EDC is quite functional--I set it to full firm on the track and it's nicely controlled, and I set it to comfort on the street. Each EDC level is maybe a half-notch firmer with the Dinan suspension. You definitely don't want to drive the car on the highway in full firm, because it's very nervous and choppy. Comfort setting on the highway is perfect.
One thing to keep in mind if you are indeed going the Hoosier route for the track--with the weight of this car and the extreme stick of the Hoosiers, the stock brakes are going to be saying ouch in a hurry. If you do Hoosiers or BFG R1s, I would at the very least upgrade the brake pads and change fluid to a high-temp formula like Motul. I bit the bullet and put on a StopTech BBK 2 months after taking delivery of the car.