If you have any good links for the non-simplified algorithm you could recommend, it'd be much appreciated.
I just looked around a bit, but couldn't find the reference I used, unfortunately. It was a really good paper though. The general topic was pathfinding in a Delaunay triangulation environment for agents with arbitrary radii. The specific version of the funnel algorithm used ensured that the agent stayed radius
units away from all obstacles, and included curved sections in the path to go around corners.
This isn't the paper in question:Link
But it does have pseudocode for the funnel algorithm at the end, which might be helpful.