That is the solution to the puzzle. It works. There is no other way to solve it. If you can't get upper left from there, you are probably missing how to chain walk across gates with key. It is the same technique you use on key flower to get to the flower.
You have to open the gate, take a step back to reset the spell, and then use it.
That's what the note in the gate maze telling you to turn back to reset spell progress tries to explain, and why that note is in the gate maze.