>end up needing a liver transplant
You won't get one nor should you get one if the reason is this.
Intentionally overdosing on Tylenol gives you a day or so afterwards to panic and seek medical attention and probably live instead of dying a horrible death. More violent means do not give you any time to retroactively back out of it.
And, yes, in America at least, some lucky people do get liver transplants after acetaminophen overdoses, occasionally even intentional ones.
Acetaminophen poisoning actually featured on two episodes of House, and one of them had the suicide plotline. In S05E11, "Joy to the World" they suspected an overweight teen OD'd on acetaminophen trying to kill herself, but the actual diagnosis was eclampsia from an undisclosed pregnancy. In S06E10, "Wilson", a friend of Wilson's suffers acetaminophen poisoning while trying to manage his back pain.
It'd be like intentionally eating death cap mushrooms.