This picture shows the approximate route from Lake Ann to the base of the chimneys. The first gully you have to find is where the first white line disappears from sight. It's not hard to find if it's light out, or if there isn't much snow around. Otherwise, it's a little tougher. You basically make a gently ascending traverse over the tallus slopes. If you follow a pretty natural line, there's a spot where the rock will come down and meet you. On the left side of this toe of rock is a gully. Climb about 40 meters up it until you're able to exit to the right, just below a short vertical step in the gully. There is a trail there. Follow it to the second tallus field.
Once you've crossed that, you have to find another gully. There are several that ascend more or less straight up the fall line to the left. If you continue past the gully in question, the tallus steepens and you wind up traversing below one cliff band and above another until, if you go far enough, the bands meet and there's no more tallus. You're lost. Go back. The gully you want is a righward ascending one. If the place isn't totally buried with snow, you should be able to find some kind of marker to confirm it. Someone actually spray painted flags on some rocks around here, but I don't recall seeing one at the base. There are a couple of steeper, cleaner looking gullies ascending more directly to the left. They might be more attractive, but they're not the route. The one you want is a bit messy and has lots of heather, grass, and some trees in it.
The first time I attempted this route we did it in November, and started in the dark. We nevertheless made it to the position of the photographer in the photo (from a May trip). This is where we went wrong. Above us was some slabby rock and a few trees... looked tough. But when we looked to the photographer's left, we found nothing but a precipitous drop with no sign of weakness. This was, in fact, the route. Up from this point was a nightmare. We made it up to the glaciers, but wasted far too much time and did little more after that than look for the correct way down. Anyway, on reaching this ledge, the climber must turn right and step down over onto a rather remarkable ledge that splits the cliff face and makes a descending traverse into the next gully. If there's a lot of snow, it takes a little imagination, but this really is the route. If there's no snow, it will be obvious, so don't worry about it. This is the spot the first ascent party called "Fat Man's Misery".
I think it's pretty safe to say that, once you're past the second tallus slope and have found the right gully to start in, you should always take the right hand option when faced with two choices.
Once you're past the Fat Man's Misery, things are pretty obvious and even if you go wrong, your variation will go.