But you opened the thread by telling us that it didn't always work. You need to work out how much more current a 11.9V diode would pass at 12.0V than a 12.0V diode at 12.0V.
The LTSpice zener model has an explicit entry for breakdown voltage. I've hand-edited Spice models in LTSpice 4, but when I just tried to do it in LTSpice XVII I couldn't get anywhere, which was frustrating.