Important note: After consulting another source, I learned that the article calls for the first pair of opposing dipoles to be fed in phase, with the second pair fed in quadrature to the first pair (but in phase with each other). Sadly, the results are the same, so I still don't know what's wrong with the model.
While attempting to respond to the question, I found that I was unable to reproduce the free-space radiation pattern claimed in the article:
Using the dimensions specified in the article for 435-MHz:
I constructed a free-space NEC-2 model with increases in source phase of $90^o$ proceeding around the circle of elements. I obtained these results with the elements tilted $45^o$ from the vertical:
The "lightbulb" shaped pattern is clearly not what the author intended, although the impedance at the feedpoint of each dipole seems to approach the author's goal, re:
The input impedance of each of the λ/2 dipoles when configured as shown will be very close to 50 Ω. Each pair is wired in series to have an impedance of 100 Ω. After connecting the two pairs in parallel, as shown in the harness diagram of Figure 9, we end up with the desired 50 Ω for the run to the radio.
Tilting the elements more toward the vertical reduces the "lightbulb" shape of the pattern, but approximately halves each dipole's feedpoint impedance:
Can anyone clue me in to what I have done wrong in the model?