I'm struggling to follow your reasoning as to why you have to look backwards to determine the cost of the path going forwards. If your weights are done correctly, getting to node D includes the cost of getting to any of the previous nodes that made up the path. Unless your movement along the terrain can cause a landslide that affects the path ahead I don't follow your line of thinking.
Correct. Yeah, if say using squared RMS (square of euclidean distance), you really pay for doing large uphills in the first place, so even something simple like that should take care of things like the one large hill + one small hill is worse than two medium size hills of the same distance problem. I was just trying to extend the problem in a different way to see where I could go with it he he he.
So in general, after reading the research on these types of problems, I've accepted that you should never break Bellman's Principle unless you absolutely have to. It's fun stuff though... there are some really interesting problems that break Bellman's Principle (mainly time-based things like traffic and music performance).