Would be interesting to measure voltage at the inverter's input terminals while a load is turned off, at various battery voltages, without solar controller and with, and at various inverter load sizes. Idea is to see if this spiking happens at other times than near 15v and without solar too.
Might also observe voltage at the controller output/battery posts for the same test times and see if there is the same degree of spiking at the battery as at the inverter input.
Just poking around like that might reveal more about what is going on
