Actually he probably needs the Daytona style nose cone more than the wing. The wings added downforce on the rear, but the car being squirrely is more than likely being caused by the front end lifting. The wing without anything up front would make that worse.
If 120-150 mph stability is the goal, blocking off the grille so the front of the car is flat (vs the inset grille) and adding some kind of chin spoiler to limit the amount of air going under the nose would probably help the most. The DC "ducktail" spoiler was also allegedly created and tested for this. Supposedly the DC spoiler was good for about another 10 mph of top speed when it was tested, but I've never seen any empirical results from that testing to have any idea how they actually figured that out.
