Having made it past these two puzzles, and the remainder besides, the first part of the final dungeon is complete. The next area I'm in now is making me think that I might have missed something earlier in the game. Because unless a certain spell which was in your inventory in the intro to the game and taken away in the ambush is actually in the final dungeon somewhere, it went missing and I have no idea where it might be. I've tried some unconventional methods to advancing further in the tunnels and have gotten stuck.
There are tunnels to the upper-left which definitely look like you need to fly through them, and the path beyond the barrier requires either incredibly tricky maneuvering with the Cane of Somaria, Ladder and Power Bracelet or that spell. Hopefully I didn't miss it somewhere back in Hyrule.