Since the white line is so thick, do I need to use a different margin? Or could there be some laminar wedge present?
Yes, sounds like there is probably some wedge material there then, if the 'white line' is so thick, but not evident in pics, poss will be after removing excess sole.
I think *generally* the breakover & edges of the hoof walls(inc 'rolling') should be put where they would be if the foot was healthy. In a healthy foot, the white line is very thin & tightly attached. Therefore, assuming your horse should have 1/8" thick inner wall material on the ground, that + a few mm leeway is about how much should be on the ground from the *inside* of the white line.