The Spiritbane and Snow's Fuser Rifle allows the wielder to have a 12in and a 48in range replacement Value.

As I understand RELICS have that power to override Normal Rules, so does this mean it overrides the chariot rules of 8in range for the passenger?

Relics over > Illusions over > Domains

I am fairly certain that the rules state the the text on a relic does take precedence over conventional rules. I believe we must perform the rite and hopefully summon the all-knowing Sigma to be sure, though.

The chariot rules are not "conventional" rules, though; they are also a set of "specific" rules, akin to Relics.

I'm not sure if I ever had an official ruling on this back in the day, but if I recall, the general rule was that "more specific" things override "less specific" things. Thus, Domains typically are overridden by Relics (but only when specifically stated; IE, if Storm Gale is in play, extending range has no effect since Ranged combat is forbidden outright).

In the case of Relics vs Chariots, I would lean towards Chariots being the "more specific" case, and thus the Chariot rules would override the Relic rules. To me, this feels right mechanically and thematically.

If I made a contrary ruling in past years, though, and just have forgotten, that ruling would probably take effect, since most of my rulings back then were made after consulting with the WizKids folks in situations like this.