Often times ice drilling is kinda ad hoc. I have really solid success with going with a 5x5 or a 5x6 starting plot and then making each subsequent layer one dimension smaller eg 5x5 becomes 4x5 becomes 4x4 becomes 3x4 becomes pray you don't have another aquifer layer or plenty of ice. I prefer channeling and ramps to stairways when ice drilling.
If you want to do the stairway route, you want to make sure you leave that tile you want your stairway as an aquifer, not channelled out into ice. So, for example, if this is what you want: (I is ice, S is stair)
IIII
IS.I
I.. I
IIII
Then when you are digging out your layer, you want to leave the spot for the stairway undesignated, and channel the rest. Once you have ice in the layer, it will look like this
IIII
IAII
IIII
IIII where A is an aquifer tile you can safely drill into without flooding.
Anyway, ultimately, I stopped using staircases all together. If you make a mistake, you need to do a whole bunch of construction/deconstruction that end with FUN, and it seemed like I things never went as smoothly as I imagined it should be able to.
BTW, slate 8th is much faster then I usually work. I'll get under the surface and walled in and such, but I will set up shop assuming i've got giant raven corpses upstairs, and am going to need to kill a pack animal. I have gotten -very- good at killing one or both pack animals while I wait for flying corpses to leave. The trick is to drop a floor tile into a water filled garbage dump, removing the ramp so you can dump your nervous tissue, cartilage, and hair into the pit and then prevent the undeads from getting out. Spinning threads isn't worth it, but tanning the hide is.