Yup, that's 100% it. In some bakers it is called "bent normal map" but it is mistake caused by some very confused artists years ago :) The vertical channel of an Object Space normal map (green in the majority of bakers) is definitely what you need here.
point helpers snapped to the vertices I've used working pivot a lot - it comes in very handy when you're dealing with stuff you didn't make and are afraid to mess with too much :D
I've been looking for info on what a degenerated face is; and how to fix degenerated faces in Maya, merging vertices with a extremely low value didn't work :(