I remember I used to have such problems, but now I don't, I can't remember what changed though... so I guess I'll just say what I do now.
One of the big things I do is make extensive use of stairs. First I dig out up/down stairs, then I channel out the stairs. The advantage of doing it this way, is the dwarves can use the stairs for access, and can channel from below. It's extremely quick to remove stairs, and provides full mining experience, so it tends to be a positive thing for training miners.
If I need to channel a deep structure - I prefer not to. I dig it out using down stairs (floors also work fine, though dwarves can dig downstairs under downstairs which is handy) and use a cave-in to smash the stairs to smithereens
Often there is no need to channel at all. Staircases allow passage and storage of liquid as if they weren't even there. So if you want a reservoir, or a drainage shaft, it can be made entirely out of up/down stairs. Staircases even allow the passage of falling objects, so you can make a drop trap out of up/down stairs - only the top z-level has to be open air. Ugliness is the only problem with doing so, functionally it all works fine (you might imagine they are tumbling down the stairs. But no. They fall straight through the stairs as if they weren't there)
I also extensively (ab)use diagonals which allow dwarves, liquids and certain kinds of actions (digging, descontruction) to pass through, while not providing support (for cave-ins) and preventing the passage of dust/vapors/gases etc.
For example using a combination of diagonal-abuse, and "leaving only the right place to stand", a cave-in can be safely released:
I want to drop the central 3x3 core. It is being held up solely by the constructed wall "w". The only place a dwarf can deconstruct this from is the spot marked "o", and he's safe from deadly dust because it cannot pass through diagonals.
#o####
##w ##
# ### #
# ### #
# ### #
## ##
######
Also while dwarves can deconstruct objects diagonally, they prefer not to. So a hatch, grate or floor can be built which allows diagonal access to an island, and orthogonal access to the mainland. When it's time to deconstruct it, the dwarves will deconstruct it from the mainland. The same is true of digging/channeling, they can dig diagonally, but prefer not to.
As for constructed walls, pay attention to build order. If you're building a box, for example, and want the dwarves on the outside, then build a northern, or a corner, wall last (they have to build corners from the outside). On the other hand if you want the dwarves in the inside, build a southern wall last. In those cases where I want to block a corridor with a wall and the dwarf will end up on the wrong side, there's nothing else for it - I just use the suspended wall trick.
I also make extensive use of temporary scaffolding, ramps, and "maintenance shafts", these get removed or walled off afterwards if required. It's realistic engineering practice and shouldn't be resented.