Is this gate driver circuit sufficient to drive a parallel FET spot welder?
It might take something like 5 μs to get all those parallel MOSFET gate capacitors charged (maybe 60 nF in total) and, during the first 6 to 8 volts of charging, one MOSFET will be highly vulnerable to taking a massive power surge of several kW for several micro seconds.
This is because there's always one device (in several parallel MOSFETs) that will start to turn on first and it will get hot on its die quicker than any heat sink can remove those heat joules. So consider what happens when one MOSFET starts to turn on in its saturation region and what the possibilities are of thermal runaway (yes, thermal runaway in several μs is a real possibility and is well-documented): -

I've marked a point on the graph above that corresponds with the zero temperature coefficient point for the IRF3205 MOSFET. As the gate is charging, if you are at voltages below the ZTC then the device is vulnerable to rapid thermal runaway. That's a typical graph so it might be as high as 8 volts. So, above 8 volts, as the MOSFET warms, it conducts less drain current and is self-limiting.
So, if the gate charge time is slow you might be working beyond the safe operating area of the MOSFET that is turning on first: -

Given that you haven't stated what the peak currents can be AND, it is pretty simple to improve the operating speed of your weak driver, do yourself a big favour and avoid MOSFET thermal runaway (aka the Spirito effect)

Spirito effect #1

Spirito effect #2

The lie they told me about MOSFETs when I was at college

Burning a power MOSFET