I am finishing this thread up with the final bits of information needed to fully understand how New Zealand rules are implemented on OGS. The two topics that remain uncertain are, 1) Game Position Repeat, and 2) Handicap.
Game Position Repeat
Does OGS’ implementation of NZ rules utilize Positional Superko or Situational Superko? I’ve proven, without a doubt, that New Zealand utilizes Positional Superko here on OGS. Actual NZ rules utilize Situational Superko.
Handicap
New Zealand rules do not award any point compensation for Handicap stones. For comparison, under Chinese rules Black gives White compensation for handicap stones, so that the area which they occupy is not counted. But under NZ rules, no such compensation is given. The rules also specifically state that Komi is not to be used.
To test this I played a match and gave Black 10 handicap stones.The final score for White reflects that no points were added to White’s score to account for handicap stones. However, if you mouse over the Captures text for White, you will see that it says it awards 10 points for Handicap. Despite it showing this, no points are actually reflected in the scoring. This Handicap data is shown for all OGS games, despite what ruleset being utilized. However, White is afforded 0.5 Komi. I realize that this was done specifically to avoid ties on OGS, but it is worth mentioning as it deviates from the No Komi NZ rule specification for handicap matches.
Note: I created this thread hoping a developer might be able to answer my questions. Thanks to users and good old fashioned research, I've answered all of my questions and have now rewritten the first post to reflect the knowledge gained, since no questions need answering any longer.