Potseal, I don't think that these are zeners, but rather transorbs, and I'll tell you why. Zeners by application are shunt regulators and they should continuously be operating at their zener voltage. That's why small ones of that size are rated at 1/2, 1, or perhaps 5 watts steady state dissipation. You didn't see 6.8V across the diodes on your good board. Transorbs of the same size are rated at 600 or 1500 watts for a very short time, and are used to clamp dangerous transients.
http://www.littelfuse.com/~/media/electronics/datasheets/tvs_diodes/littelfuse_tvs_diode_1_5ke_datasheet.pdf.pdf
If you look at the Littelfuse datasheet, you'll see that the 1500W is for <2mS. (Fig.2) But the steady state power dissipation is only 6.5W. That should make sense if you take a look at a 5W, 6.8V zener and compare physical size.
I'm not saying that you can't build a shunt regulator with a transorb, or a clamp circuit with a zener. You can. They just wouldn't be optimized for what you're using them for. So for a zener, think,"regulator", and for a TVSS, transorb, MOV, crowbar, think, "clamp", and "protection".
Joe