Make players slide off ledges if they're stood too close

I have a ragdoll system that turns your character invisible, creates a duplicate of the character to serve as a ragdoll and tracks the location of the player. This is all so player states remain unaffected, so I can reuse fall damage code that requires humanoid states to function. This works great, with the only exception being that if the ragdolled player is stood near a ledge, they will not fall off of the ledge.TuVNAgqbY8

Here is what happens behind the scenes.
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So, how exactly would I make the player slip and fall off of the ledge without interfering with the player’s humanoid state?