This one felt suspiciously normal, and for a while I was wondering when the subversive element was going to drop. I made my way through the dungeon, entering via the cave and exiting via the forest below the town. I didn't even realize the forest entrance was secret because I wasn't paying enough attention to the tiles, but nonetheless, that made me suspect that finding alternate entrances to the dungeon was going to be the key to winning. I explored the upper part of the map and was confused to find absolutely nothing. When I went back to the forest entrance and couldn't find it, that's when everything clicked in a really satisfying way - the seemingly useless upper area, the weird requirement to press the action button to enter caves and stairwells....
After dying to a Hundred Heads, I figured I'd try to guess the location of other entrances on the world map, and my suspicion that there'd be one in the otherwise-empty upper mountainous area proved correct. From there it was pretty straightforward to finish the game - I stumbled upon the Iris Tapestry pretty close to that entrance, and while I took another death to a Hundred Heads due to a lack of resources, I pulled it all together on my next run.
I was surprised to read that there were only two secret entrances. I thought I had just lucked into finding the one right near the treasure.