You can get my input here.
I started out with the same idea as you described (which is IMO significantly more involved than the code you linked, where you merely cancel out n/s ne/sw pairs), and I do feel that this might lead to the solution. However, while thinking about the problem, my thought was that this will end up being somwhat complicated, since we have to do iterative substitutions, since once you blend two instructions, you need to recheck the blended instructions against all the other ones (even the previously checked ones). I do feel that this should converge into the outcome with minimal steps, but it felt like too much work. Perhaps it was too early in the morning for me to properly think it through 
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So instead, I did some research and found the linked article. I find the approach in that article quite elegant, as we need to pass through the input once, keeping only the current position as the state, and we don’t need to do any post-processing. Based on that property, I was able to build a purely streaming, forward-only solution with constant memory usage
