Playing you demo in Lite-C, I cound only find one little part, where the entity got stuck.
(not really stuck, as it could move back), normally it moves fine.

Your problem is not really related to the BSP architecture/collision hull , but rather to a bad movement code.
You let your entity slide on te ground.
If you would walk in daily life like that - sliding with your feet tied to the ground -
you would trip over every edge in the carpet already.

You should write a better movement code:

First: lift a leg up. (move the entity up a certain amount)
then move the body forward (move into heading direction without movement in hight (z))
then take the leg down (move down the amount you moved up + the acceleration by gravity)

this way little edges on the ground cant make the entity get stuck anymore.

In the showcase I have a demo with an advanced movment code that is
not hard to transfer to Lite-C.