And don't auto-tie each save type to a stat - have the specific effect state whether a stat applies to a save or not; and if so, which one. Example, where three different things are forcing a death save:
Banshee's Wail: death save, Cha applies (or Wis, depending which stat "strength of soul" resides under this week)
Deadly Poison: death save, Con applies
Massive Damage: death save, unmodified.
One could in fact easily make an argument for there being more than 6 save categories, especially to break out the catch-all "magic" category into smaller bits. There might, for example, be different save categories for area spells, targeted spells, psionics, and devices; and-or to account for whether the effect is arcane or divine in origin.