OP you won't have any issues putting a regular street tire up front and a drag radial in the rear as many and myself included have done this.
I put 20x10.5 factory rep wheels from PK Auto on my car in the rear with 305-35-20 Nitto 555R2 drag radials and put a 275-40-20 stock size setup Continnental Extreme Contact Sport summer tire up front.
So technically a staggered setup. I've had absolutely no issues and it did not affect the drivability of the car.
If you want to stick with the factory pirrelis up front while having your drag radial in the rear that's absolutely fine. Like I've mentioned many folks on this forum have done that with no issues.