Horizontal Stacked Bar Chart Difficulties

I'm focusing on creating the stacked bar chart and not worrying about all of the other elements in the picture (data labels and such). You are correct that a stacked chart adds each series together, so the usual first thing that is needed to create a stacked chart is a helper range to compute the differences between the different values. To do this in your file, I:

1) In A7, I entered =A2 and copied/pasted that into A7:A9 and B6:E7.
2) In B8, I entered =B3-B2 and copied/pasted into B8:E9.
3) Select A6:E9 and insert a stacked bar chart.

That should create the desired stacked bar chart. You can format various chart elements and add and format data labels and such to get something closer to your picture. Note that I am assuming that "leading organization" will always be larger than "average." This will become more difficult if you cannot know a priori whether average or leading organization will be the larger value.

Does that help?

I used a clustered chart with the series overlap set to 100.

You do have to change the order of the data so Best possible is the first series.