ABW
Think of a wedding cake as a very simple grading plan. The table is the existing grade. Each layer of cake represents one foot of fill. The area of each layer, times one foot, gives the volume of that layer. Add up the volume of each layer to get the total volume of fill.
Now look at your grading plan. The existing contours are the "table", of course they are never flat. Pick one contour elevation and trace the existing contour with a red pencil and the finish grade contour with a red pen or marker. The area enclosed is just like a layer of the wedding cake. Measure this area with a planimeter. Of course there may be more than one area enclosed, because there can be both cut and fill. The points where the red pencil and red pens lines cross are your daylight lines, where you are either matching to existing ground, or transitioning from cut to fill. Now do this for every different contour elevation on your plan, using different colors (I usually start repeating colors every 5 contours, there just aren't enough colors to do a complex grading plan with all different colors). Draw daylight lines through all of your daylight points to separate cut areas from fill areas. Measure each separate area of cut and fill enclosed by the same color, (use highlighter to separately color the cut and fill areas) multiply the areas by one foot or your contour interval, to get the volume of each area of cut or fill. Total up your cuts and fills. Don't forget to apply shinkage corrections. Also, if your grading plan contours are drawn to finish grade, don't forget to correct your cut and fill quantities for the volumes of subbase, base, pavements, concrete, etc.
While this is a difficult procedure to describe in words, if you were here I could illustrate it to you easily. I believe it would be less tedious than the method you are using, although any earthwork method can be tedious, even the computer generated ones.
As I described in the previous posts, I have done this procedure on AutoCad, although it is just about as much work to do it on the computer as to do it manually. I have found that it gives very similar results to the grid, composite and average end area methods which the Softdesk programs generate, when everything is done right.