I was mulling over a solution for this and I think I came up with a pretty good one.
Here's the modified Godfather page I made:
https://wiki.sc2mafia.com/Userysop/Godfather
As well as the modified Dragon Head page:
https://wiki.sc2mafia.com/Userysop/Dragon_Head
If you look at the source of the Dragon Head page, all it does is set the variable "triad" to 1 and then displays the Godfather page as a template. This variable is key. If you look at the Godfather page source, you'll notice that I've replaced all the Mafia-specific terms with template pages such as
https://wiki.sc2mafia.com/Template:Us.../NameGodfather. These template pages have code that checks if the triad variable is set, and if so, then it displays the Triad version of the term, and otherwise displaying the Mafia version of the term. I've also modified the infobox in the same way to control what color is shown (
https://wiki.sc2mafia.com/Template:Us.../Infobox_mafia). This way, any changes made to the Godfather page will then change the Dragon Head page too since the latter just displays the former. The only issue I've seen so far is when the page says "a Mafioso", since it changes to "a Enforcer" which isn't correct. I haven't thought of an elegant way to handle this yet, so if you have any ideas I'll be glad to hear them.
Once that's fixed, all that's left to do is go through all the Mafia pages, replace the necessary words and links, and then set up the Triad pages accordingly.