Clamping negative voltage on comparator input (LM393)
You could use a Schottky diode, at the currents you're running it should stay in the 0.3V range.  Alternatively (or additionally) you could put a resistor from the positive input to ground, creating a divider that will keep the input in the recommended range.  This will also reduce the voltage seen on the positive half of the wave, so you may want to modify your REF accordingly.