PROX improved on what I was doing by backing up as he was shooting the reactor. This gives the mech a false floor right by the other mechs. Simply turning around makes it a lot easier, but you need to shoot the Gargoyle as quickly as possible before it jumps out of the Jump Ship and flees into the outer depths of space.

I changed up the weapons again, this time putting the AC20 back in with the LBX to balance it out. I found that much of my ammo was utterly wasted, so I put it back in to counter that problem. It made taking the reactor out much quicker and more consistent.

I can't advocate this for a full run; doing it this quickly is hard.