Made my way up the mountain again, realising I’d missed some obvious blow-open-walls bits (and hence why I was stuck). At the top, I found a Minish Mine, where a blacksmith took the broken Picori Blade and send me off to get the Fire Element from another nearby mine.
Naturally, this was another dungeon. The mid-boss was a load of grey spiky wobbly things, and the weapon in this dungeon was the Cane of Pacci. How unfortunate. It flips things over. So, after getting past some lava pits and did mine-cart riding, I killed the fire dragon end boss thingie. Hurrah! Fire Element is mine.