Phew! It is finally working!
Thank you dc42, for patiently putting up with me!
I added:
A secondary mosfet in parallel (unrelated to the problem) to distribute the amperage draw,
two decoupling capacitors (100?F and 1?F) to the source of the mosfets,
a reverse protection diode to the power input for the whole circuit,
a 1k resistor between the Arduino output and the TC4429 input,
and I reduced the pwm to 25kHz just in case.
It works beautifully!
THANK YOU once again!