Thanks for your kind and insightful comments. About the nature of the game, Mark Brown came up with the distinction between puzzle games and problem-solving games in one of the really old GMTK videos, if you haven't seen it and are interested in watching an analysis.
The little secret about this type of game is that the levels are much easier to design. Instead of having to come up with a puzzle that is built around a particular path, I can just plop down some terrain and an objective and say "This level is left as an exercise to the player" (obviously I checked each level to see that it worked and wasn't too annoying, but I didn't have to do any rigorous testing to rule out unintended solutions). I actually didn't get the game working until around 80 hours into the jam, but after that I banged out the full set of levels in just 4 hours.