Did you read the datasheet for the mosfet ?
If you read it I think you will find that you need -10V to turn it off.
That's been your problem since the beginning. Only a logic level mosfet will turn off with 0V.
Most require at least -7V to turn off.
If you try connecting -10V to the mosfet gate I think you will find it turns off.
The TC4427 is not a bipolar device so you would need one that runs off a +/- power supply voltage.
The TC4427 has been a waste of time if you are trying to drive a mosfet that requires a negative
voltage to turn off. Try turning off the mosfet with a 9V battery connected with the "+" to GND.'
I don't know why the TC4427 won't turn off the led but I believe that is a different issue than why it
won't turn off the mosfet.