I personally dont like the button mashing because it wakes my wife up as i can get "into it" but its still fun.
What i feel is lacking is that Jason can go instant kill. If they added a 2 or 3 second animation of pamela talking to jason, it would allow counter play. The duration should shorten as jason's rage increase. The amount of clicks required can be dictated by a combo of stats like OP has said. Additionally as rage increases the window would decrease. During the last 2 minutes only a pocket knife would interrupt or a slow deciding jason. During this period Jason should be able to manuever and select a kill type.
I think interrupts should be possible but with risk and reward. If other counselors attack jason there could be a small chance that he drops the current counselor and grabs the attacking counselor, or a chance for the counselor to injur themselves, or expend significant stamina. Also jason could use the current counselor as a shield.
Another layer could be different weapons have different outcomes. Blunts can stun, while blades make him stumble with less recovery time. Guns should still work as is, and flares and firecrackers would require a direct hit, and only increase the animation time but not release the counselor.