We're all just guessing right now, we need a lot more information to provide any useful advice.
One thing that jumps out is that if the current sense resistors total 200-300mOhm (not 0.2-0.3mOhm as originally stated), that means that at 15A the source of the low side switches will be at 3-4.5V, which, depending on the gate drive situation, could mean you get "free" current limiting, or with enough d/dt and the right parasitics, something that rings like a bell and blows up.
Can you show the layout, some scope traces, and ideally a better schematic? Are these "inrush" events (really, repetitive pulses from what you've described) caused by the load itself, or a result of the supply fluctuating, or are they induced by the way you're driving the load?