I found a cubic equation that fits the data in the paper with an R² value of 0.999264, which is phenomenal. It is:
0.7225x^3 - 4.48536x^2 + 8.96214x - 3.578
Where "x" is the zone number.
This works regardless of how your zones are setup, meaning their percentage differences don't need to be strictly increasing.
For example, if I spend 100% of my time in a zone, the PPi values for my #running training zones become:
Zone 1: 81.64
Zone 2: 46.65
Zone 3: 41.79
Zone 4: 54.58
Zone 5: 235.86