I see this problem lots when testing comparators, here are my thoughts on the matter..
1) Hysteresis really is the best way to do it - try tying your output to a little resistor divider to gnd (10 Ohms). And take your inverting input from there.. When your input is below GND, output will be GND and resistor divider will have no current flowing.. Once it switches though, it will need to go a little farther past 0 to reset the circuit. This keeps most comparators snappy, although ANY COMPARATOR WITHOUT HYSTERESIS will have a region of oscillation.
2) Add a resistor to the output - 1k, 5k.. This will pull a little current out of the comparator output and reduce the location of the first pole in the comparator's frequency response.. This should help for slow-rising signals, but for very slow (1mV/sec) you will need a very low resistor and waste a lot of power.
3) If all you want is 0-cross, use a diode and a 1k pulldown. This will be ground when the signal is below 0, and high once you pass the diode turnon voltage - 0.3v for shottky. Can use this as the input to two inverters to give a sharp, noninverted output. But you will have a 0.3v offset. No big deal if all you want is timing info, as it happens at the same point every cycle - but if you need to turn something on at 0-cross, remember this cheap solution gives offset.
4) MAX912 uses bipolar or single supplies, has TTL output and only 7ns prop delay. Maybe try this instead - go to
www.maxim-ic.com and request some free samples.