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I started with a bomb wand as usual, then found another one right away near the entrance of the Mines. So, I decided to bomb some stuff I normally run past and discovered that there was an Outside part that I could get to with a little more bombing. So, there is in fact Outside both to the left (which is easy to get to) and to the right of the starting spot.
(I'm going to post this set in reverse chronological order for the benefit of those scrolling down.)