First of all, if we're trying to emulate the Prism gadget, it's supposed to start clamping at 18dBU, not 18dBV. 18dBU is 17.4 volts peak-peak. Since each zener in the back-to-back pair clamps one half of the waveform, we're interested in the PEAK voltage, which is 8.7V. Subtract from this the FORWARD drop (0.6V) of the other zener diode that's in series with the one that's "zenering" at any given signal peak and that leaves 8.1V. 8.2V seems to be the closest standard zener value.
The clamp should go between hot and cold, not between hot and ground and cold and ground. For reference, we're talking about the sort of circuit shown in figure 5A of that Headwize link. For balanced use, you'd split the value of the current-limiting resistor R1 and place half in series with hot and half in series with cold. As for the value of R1, that would be chosen to pass the desired current through the zeners at the point they begin clamping (thus affecting the "knee" characteristic) without presenting an excessive load to the driving device. It's not a good idea to run a clamp like this without current-limiting resistance since when it's limiting, it's essentially shorting out the output of the device driving it :?
As an aside, I wonder about their choice of 18dBU since a system should usually be set up with 20dB of headroom above nominal operating level, which would mean a clip point of greater than +24dBU in a "+4" system. Perhaps they made the knee so soft that they needed to set the initial limiting point several decibels lower than that to ensure effective suppression of +24dBU peaks.