Using higher voltage MOSFET will only result in higher amplitude spikes. At 20A the coil likely has some significant energy in it and transferring that energy to maybe 1nF of capacitance in the FET and cabling will consequently produce a spike up to hundreds or thousands of volts unless something breaks down before.
The relevant MOSFET spec is maximum avalanche energy at Tc=100°C or whatever the ambient is. A freewheeling diode would help too if it can be fitted into the circuit and if there isn't one already there, I would check that first before assuming that FETs are dying from breakdown.
IRLR is a logic level FET, which means it works with 5V gate drive and this could be the reason why it is recommended. Check if the driver works at 5V or 10V/12V.
Compare figure 1 in the respective datasheets and you will see that while IRF1010NS is capable of higher current overall, IRLR2905 has higher conductance at 4.5V or even 5V gate voltage.
The reason why IRLR2905 keeps blowing up may be dV/dt. 13A is 13nC/ns, this flowing into 400pF=0.4nC/V produces voltage rising at 32V/ns, well above the 5V/ns maximum allowed. Additional capacitance would slow it down to a safe value and there may be additional capacitance already there.
I typed that pump number in google and found people mentioning IRLR3636, which seems to be better in pretty much every way.
Before installing anything, make sure that the driver and gate resistors/diodes aren't blown.