Specifically the questions where it gives you multiple kanji and you have to arrange them in from least to most strokes. Is it possible to change the drop down list of numbers to a box where you can just type in a number? I use an IME and a tablet, so I have a pop up window I draw kanji in, and when I have it in a comfortable position to write it covers up the lists of numbers when they drop down and I have to pull it out of the way to select a number. Since the system doesn't even looks at the numbers you enter anyway, just the order of the kanji, this doesn't seem like it would affect anything.
This word be good for my iPad as well, since dragging doesn't work there. Would also work well for those with limited motor skills and can't easily drag the mouse.