Playing Mah Jong since 10 (I'm 51 now) I really love your Wiki: the layout is very compreensive, sistematic and a pleasure to follow.
Knowing the western style and chinese old style (note I don't call it "Hong Kong" - I learned it 30 years ago from a colleague from Macao and it's played by many chinese comunities all over the world) fairly well I'd just wanted to offer my two cents…
It seems your only source of info is the Amy Lo book along with the 9 dragons and 4 wind software. There are other books on the subject, mainly Pearlmen & Chan's "The Chinese Game of Mahjong" and Constantino's "Let's Play Mahjong".
The system of scoring is pattern-based and may be categorized in three types: "Fan" type, "Lak" type and "Poon-Lart":
- The first one (absent from your pages) is a geometric progression allways doubling score for each Fan: "2-Fan" is the system traditionally used by begginers and for quick (not gambling!) games since it's easy to memorize and apply. Its main problem is that after 5 Fan scores get too big. So, veteran player groups who routinely get higher Fan prefer to use one of the other systems.
- The Lak type (1st and 2nd variation in your pages: only one was enough!) uses "steps" in higher Fan (higher then 4 or 5 Fan and groupjng two or three Fan together, depending on the preference) grouping two ou three fans together in order to lower (limit: "Lak") the higher scores. The main criticism is that getting more one or two Fan more in score sometimes doesn't get the rightfull reward (it's a "stepped" progression).
- finally the "Poon-Lart" type; it's the used system in most chinese gaming groups (your "3rd variation") and consists in halving ("Poon") some values of the Fan in order to get a less steep progression. Another well-used alternative progression different from the one in your pages is 2-4-8-16-24-32-58-54-96.