Ok! I finally, finally figured out the solution that I assume was intended. And actually, once I figured out that one, there's another solution that works in very much the same way, but with a different final configuration. I had sniffed around those approaches when I was trying to figure it out initially (with the covering of something important), but there were just a few subtle pushes I missed that made the difference. Nice!
But those two solutions are distinct from the one I used the first time around. I get the feeling from your note that you haven't yet seen the way I solved it. Now that I see the intended solutions, you could eliminate my solution without ruining this puzzle (though doing so might guide the player just a bit more toward the intended solutions). As you were comfortable with the hint you gave me, my solution also involves the covering/uncovering of something important.
Whether 25 or 27 seems harder probably depends on what you think of my solution, and I won't spoil more than that until you give me the word. Perhaps you'll want to keep it in! After all, even as the puzzle is now, I think I spent the most time in this game on either 25 or 35.