As I understand it increasing rotor speed to increase tail rotor thrust for a low power problem (Low power balances stuck tail) will only have a limited benefit. Too much increase in rotor speed will exponentially increase rotor drag for the lift gained requiring more torque to keep rotor speed....but you are trying to keep torque down so a small + but too much and you'll be into the -'s.
Using a little more power and opposite cyclic to counter the yaw and using a cross wind to counter the resultant drift may get a reasonable run on speed and ROD if not I'd go for an engine off (My auto's are probably survivable)
ps. The Sea King has had several snapped and jammed cables as well as a drive failure or two