You can power through every aquifer level except the last much more quickly by using this modified method, then switch to the above method for the last layer.
The setup is similar, but instead of channeling, dig down staircases for the slits, then up/down staircases below them that will fill with water. (Multiple levels shown, color-coded for convenience.)
Install the pump as before, but annoyingly you must remove the stairs from its input tile (on its level) for it to work. Pause/one-step until there is no water in the tile the pump is drawing from. If the layer revealed below (yellow) this is not an aquifer it should be dry during this frame (not tested), and you should switch to the original version. More on the conversion below. Similarly, if there is an aquifer but it looks like one of the slits won't drain into an aquifer based on the revealed material (yellow) you may want to switch methods and consider your options for dealing with the non-aquifer rock.
With the pump active, dig up/down staircases 1 level deeper into the aquifer. This will act as a drain.
Re-construct the pump facing the other direction, remove the blocking staircase and repeat.
Stop pumping. You don't need the pump any more for this level.The water will now simply fall down the staircases. If you build these walls in this order you may not get a single cancellation!
Carve out the center with staircases and mining (Don't carve staircases in the layer below!). The first of the 4 walls will push your builder all over, but it will get easier.
You're ready to conquer the next level! When you reach the last aquifer level, you can switch to the above method by building ramps in the slits. You can build the ramp directly on the carved up/down staircase, but remember dwarves can't use the ramp if there is a staircase directly above it. You may have to remove a ramp to build a wall in the slit as part of the above method.