I have ordered the parts—they should be here in a few days.
I will use a heatsink, connect the 10k pulldown to the TC4429 input, and use a resistor value below 50 ohms in between the TC4429 and the mosfet.
In theory, if I did pull the gate of a p-channel mosfet to ground, would that not turn it on rather than off?
I am doing my best to grasp all of these details but sometimes my head hertz! 
I will report back when the whole thing is installed.
Thanks everyone.