Really solid entry! The way you incorperated the theme into the mechanics makes for really unique gameplay, and the puzzles are a real challenge! But a fun one. The difficulty curve is perfect (though I did gets stuck on the first jump for a while, but that's probably just me xD), and the little tutorial illustrations are a great addition. And like others have mentioned, this game really shines in charm. The aesthetic, the art style, the little facial animations and music... it all comes together so well!!
The only thing that bugged me a little were the switching controls. There were a lot of times where I thought I dragged the block to a connectable place (adding an X to non-connectable places is a great touch and much appreciated!) but the block would just snap back several times, to a point where it got a little frustrating. Since the block positions are very directional (up down left right), perhaps it would be better to click+hold the block with the mouse to activate the switching sequence, and then use the arrow keys to position the block, so it snaps right away. Alternatively, if you keep the current controls, maybe you could just add a little visual or audio indicator that the block is placed properly and will snap. :)
But that's just a tiny tiny little suggestion on an otherwise wonderful game. Congratulations on getting such a polished, fun result in such a short time!
Best of luck in the jam!
-Sasha