Hey @shinshiner!
Unfortunately, unless the animation is physics based, adding physics collisions would not be able to solve the problem as you saw from using physical simulation.
If all else fails, creating a copy of and tweaking the animations themselves to compensate for the structure of your character will most likely be the best option. You can do so using the animation sequence editor.
You can find more information here:
I hope this helps point you in the right direction!