You have great guitar. Now, the next most important thing here is good and certain amp. Pickups are not so relevant. People used to play jazz on electric guitars 60 years ago and hard rock 40 years ago with less defined pickups than you have or you can find at shop nearby. MHO is each guitar can play jazz and rock. It's the beat that separates music styles.
I have 498T/490R combo. 498T can play everything but Fender cleans. 490R is great neck pickup which can also be put in bridge position. Both are quality made as yours so just adjust p.u. height and the amp.