Although I do like applying damage to other stats where appropriate, I don't actually think you need to if what you're worried about is balancing them.
STR is the more important attribute if you're consistently getting into combat. All these games share an ethos that combat shouldn't be a hugely frequent thing at the table. In that context, the stats are a lot more "balanced". DEX is by far the most called for Save, in my experience, plus it's how you go first in combat.
WIS/CHA is a little trickier, depending on your individual campaign. Although in Mausritter specifically casting spells can cause WIL damage.
FWIW this is something I grappled with a bit for my own Odd/Cairn hack (slightly exacerbated by some other rules changes), and I eventually came to the conclusion that I didn't need rules changes to fix it. The only thing I really plan to do is make sure the included bestiary includes examples of damage to other attributes.