10ohm is not enough to dampen the gate charging. Just looking at the datasheets, an input capacitance of 22pF on a 2N7002, with 10ohm and zero source impedance, and given a 3.3V rail you'd be looking at a rise time of 1.1ns from 10mV to 1.8V. Peak current would be 320mA at the beginning of the switch - which clearly the TLC3702 can't supply. The TLC3702 has an absolute maximum output current of +/-22mA. This means you need a much bigger inline damping resistor than 10ohm; a ballpark figure of 220ohm would be a better choice, yielding a rise time of 25.1ns and a peak current of ~15mA for the nominal specs, but the easiest way to find a good value is empirically - just see what works well, and in your case give it a little extra to keep things nice and quiet in face of individual unit variation (unless it's a one-off).