The cage was a bust, so the wool is somewhere else, probably in the middle. Before anybody goes looking, the gear needs some work.
Iron for days
All the stuff is beat up. Luckily one of them has levels and iron for days, so everything gets fixed up all the way. The other comes into the hideout, which turns out to be an only-me spot, to fix his things too. There's a junk pit next to it. Someone threw flint, arrows and feathers down there and now needs arrows, so in he goes.
One of them puts on the other pair of pants and offers his old ones to the other, whose pants have no magic. They're a bit snug, but they'll work. They stop smelting iron because it's easier to carry as blocks. There are 23 chicken in one inventory, and a stack of bread is on offer. Somewhere in here it comes up that if they had done this area first, before the end area, they'd have had a bunch of diamonds and a lot of the game might have been easier.
Around the edge
The choice is to explore the middle or keep going around the edge. They say welcome back and go around the edge. A single block of iron sits where something exploded. One of them puts on his boots of escaping. So many skeletons. Then one of them announces he's going to do the thing the other loves, where he runs really far ahead, and if he dies, that's why.
Some chests out here just hold stacks of iron. One sits on a little peninsula and turns out not to be trapped. They catch each other in a crossfire at least once. A witch gets the business. There's TNT above them, and then, from the edge: I see the wool. White wool. They want to circle around some more first and then water their way closer.
A bed up the hill
More TNT, more blazes, another quad spawner. One of them has a Smite sword, which is why that isn't working out very well. Blaze spawners go down one after another. There's an emerald in the floor, and one of them goes after it. Later he admits he didn't get it.
The wool is up in a pillar, so they start water-bucketing the whole area under it. Nobody wants to die in lava. Something that looks like TNT turns out to be gravel. It's a long run back every time, so a combat bed goes down up the hill, with a request that the ghast not blow it up. The plan for the wool is the same thing they just did for the cage: blocks, ladders, straight up.
The platform up top
The platform they're heading for has a blaze spawner, a creeper spawner and a skeleton spawner on it, and at least three creepers walking around. One of them is glad he still has an Infinity bow, because one of these things just doesn't want to die. A creeper spots the one in front. If things could be any worse, it'd be right now. The creeper gets shot. On the top spire there's a ghast spawner, and they can see a creeper spawner too, and that's where they stop.