The flaw with Mark of the Odd games

Hey all, games like Into the Odd, Electric Bastionland, Mausritter, Cairn, etc. All use Chris McDowall's elegant 'stats as health' concept.

It's a great concept: It keeps the character sheet compact, and links a character's prowess to their condition which is very immersive.

However, there's a flaw in this system I cannot ignore: Strength is by far the most important Stat as almost all attacks target a character's Strength. As a result Dexterity and Will/Charisma damage rarely comes into play.

Whenever possible, I try to apply Dex damage from attacks, traps or poisons that hinder movement, or Wil/Cha damage from spells or poisons that don't affect the target physically, but that's just a houserule and it's not always easy to come up with immersive reasons a foe would have these abilities.

How do you get around that at your table? What are your most common ways of targeting these stats?