How about being able to pick up other hearthlings? Maybe some kind of check of the lifter's sqrt(str*dex) vs. the lifted's (str*con), or whatever functions would scale properly, and the lifted person always has a more or less random chance of struggling free if they want to...
Imagine picking some one else up in the middle of a fight and dropping them into deep water?

One could also introduce a battlefield triage/medic dynamic in some scenarios, to carry your KO'd buddies away from rangers during a siege or something... The stronger you are, the faster you can run with your fallen comrade (at least for a short while), hoping the archers stay behind their walls and don't follow you.
Feel free to yell at me if this should have had it's own thread, but i figured it fits in to the whole lifting/running debate.
"Bein' a minotaur is a lot like bein' a regular human except moo" - J. Rowland