I have not read Kageyama, but ladders (and other similar positions) are near and dear to my heart.
I see ladders similarly to the way Bill does (though I make mistakes more often, I guarantee; stones are hard to visualize ... more on this later).
It's interesting how many people use the "tic-tac" method beyond 4-5 moves ... I can't keep "tic-tac" up past the first 6 moves or so ... I lose my train of thought, and sometimes miss.
To elaborate a bit on my ladder reading style ...
1) Diagonal lines
The simplest ladders are diagonal lines. I don't visualize stones very well, but I can see a straight diagonal line.
Don't know why there's a difference, and I'm slowly getting better at using stones instead of lines.
2) Partial shift
There are certain shapes that indicate to me that it's possible to "shift" part of a diagonal line in the up-down or left-right directions. These are the next step of complication in ladders, in my opinion.
3) Reflect direction
After getting good at the partial shift, the next thing that I started to see were shifts that allowed a right-angle turn for the diagonal line. This seems to me to be the next step of complications in ladders.
From here, my ladder reading gets better by recognizing and visuallizing opportunities for throw-ins and eye-stealing tesuji as triggers for ladder situations.
My reading is imperfect, but I feel comfortable reading sown a narrow line of play fairly deeply. Breadth of reading is slowly getting better.
Now, if only my global strategy were to get better ... I suck at reading the state of the overall board.
