40N10L is 100V 40A logic level MOSFET. IRL540N is 100V 36A, so it is OK for replacement.

Is the diode at right flipper coil properly connected and working? Sounds like the inductive kick-back from coil destroys the MOSFET.

The driver board gives a 40 ms power pulse to flipper coil when flipper button is pushed, and after that a 1ms pulse every 12 ms while holding the flipper up, and if the EOS switch is closed it will give a 40 ms pulse again.

This pulsing will cause inductive problems if the diode is not connected, but since you verified that, it should be OK! I think there are only two reasons for Q16 to instantly burn out - either the diode is open, causing inductive kickback, or then the coil is partially shorted, exceeding maximum current of the transistor.

Since the coil seemed "soft", check the coils resistance and compare to left side coil. It is strange that the IRL540N did not burn out while the 40N10L did.

Unlikely the problem is in 74HCT273, since the coil is not continuously on, but only after button push.

Edit: I see you have checked the resistance to be OK. Maybe then you could try replacing the '273 and the pull-up resistor / filter capacitor between '273 and Q16?