This is me just bouncing an idea around to see what you all think. So, don't get super bent out of shape because it doesn't adhere to the movies. I looked and didn't see anything similar so here it is.
What if they added a young Jason to play as? He would be a new playable Jason and would have to have a completely different play style and abilities. Think how creepy it would be to be chased around the woods by some deformed killer child.
STATS
Strengths
Can run - same speed as slowest counselor
Sense - lasts longer
Hide - can hide like counselors
Weaknesses
Water Speed - This Jason is very slow in the water
Weapon Strength - This Jason can deal less damage with his weapon against counselors.
Less Hit Points - This Jason has lower HP than other Jasons
ABILITIES
Shift modified to a fast run. Just creepier
Leap replaces Stalk. Can leap a good distance to close gap or if in range jump on counselor.
Stalk would be a permanent passive ability that only cues music if seen and stops once he's so far away.
Young Jason would also be able to climb through windows. He's not a brute he can't just bust through a door. Unless maybe he leaps into it.
WEAPON
Scissors (Updated - SexDrugs&Tea)
Sickle
Would probably require a lot of time to work out how to do it, but would be creepy and awesome to be chased by a fast child Jason.