Player fall away from mountain edge without slide?

So, I am using the enhanced FPSWalker script from the unify community. And I have my player slide when the slopelimit is reached so he slides down steep things. But, I really want to find a way for him to actually fall off a cliff. I have an extremely tall mountain face, and when he steps over the edge he literally slides down the whole thing, and this prevents an actual free fall or fall of any type and prevents fall damage. The fall damage I have works only from straight impacts downwards and with this slide it does not happen. If I take off sliding he will unrealistically fall a few feet down the mountain, which is worse.

I have been theorizing in my head on a script for him to have extra displacement from the mountain (x or z i guess) so that he falls away from the mountain.. Kind of like that one game Just Cause 2, if you have played it, the character falls away from the cliffs by a little bit, and starts to free fall. I am making a FPS so the character does not need to rotate forward, or ragdoll down the mountain, but simply fall away from it so that he gets a good fall time (I'll be adding a wind sound for this and then of course the player gets injured according to my damage script like he should on impact)

My main question would then just be how I could begin to create a script that will push him away from the mountain? Maybe, using his last movement and increasing it? (Like if he moved left right forward or backwards off the cliff, then increase that distance so he falls the right way off)

Thanks for any help in advanced! :D