Diode Strings I-V Curve questions(cont)
Forget about spice models and simulation and think about what's happening instead.  First, the curve shows significant current changes below 1V even though you have 6 zeners and one forward diode in series.  Second, the zener chain should eventually look roughly like a voltage source although your plot shows it is acting like a current source.

You didn't say what voltage the zeners are, but I suspect that the sum of their zener voltages is well above the 10V your plot ends at.  That means your plot is showing the leakage current.  That also explains why it's showing a current source because diode leakage current can look largely like a current source in that part of its operating range.  The leakage current is a function of temperature, and light hitting the junction if the junction is open to illumination.

What you should do is run a plot with a current source, not a voltage source.  In other words, control the current up to maybe 10 mA and see what voltage you get.  That will show you how these things are normally supposed to operate.  If you want to understand how a zener diode works, it would be better to just use a single one without adding the confusion of additional zeners and a ordinary diode in the mix.