Thanks for that fine diagram. Before seeing your details I was speculating that you were using higher-voltage MOSFETs, which have a nasty tendency to RF oscillation when biased for linear operation with Vds more than 10V (the oscillation is internal to the MOSFET and often cannot be stopped even with a gate-source bypass capacitor. I have not experienced this problem with low- voltage parts like your IRFP2907 and IRF1405, but it is still a possibility and, depending on wiring inductances, could mean that your FET may be exposed to excessive RF gate voltages. However these RF oscillations (10 to 30MHz) are easy to see on the scope.
I think it's more likely you have a power dissipation issue, and are exceeding the MOSFET's junction-temperature spec. You can do all the calculations you want, but the bottom line comes from a complete set of careful thermocouple measurements. Watch out for gradients across the MOSFET's case. Most of the power-supply big boys use strong clips placed on the MOSFET's plastic housing to evenly press the case against the heat sink, rather than screwing the MOSFET down by the tab, which can lead to a slight tilt to the case. Hmm, I wonder if this can lead to a stress on the silicon, lowering the degradation and failure junction temperature?
The big boys also use higher safety margins, e.g., four MOSFETs instead of two.
One thing that raises my eyebrows is your low 5V supply voltage for the LT1013, which limits the MOSFET gate voltage. According to the IRFP2907 and IRF1405 datasheets these are not logic-level- drive MOSFETs, and they may need a Vgs of nearly 5V to operate at 15A, which the LT1013 may not be able to deliver with Vcc = 5V.