The game should have a few of the Jasons have a feature where they don't automatically play intense music when he's near a counsellor. The player playing Jason can only trigger the music by themselves, which will then raise the fear level of counsellors within a certain range. Jason can be more stealthy and do more hiding, striking only when an oblivious counsellor walks into his vicinity, just like in the early movies. To compensate for this feature, his other stats would be reduced significantly.
This feature raises the suspense since counsellors will never be sure of where and when he is going to pop up. It also makes for less careless gameplay since the counsellors will have to be very aware of their surroundings at all times.