Working with a lot of text in Illustrator is often tedious. Your project won't be any different, but here's an idea:
You'll need to create your own circular baseline text grid.
Draw a ton of concentric circles over your pie chart and then cut them into the "pie slices" you need for EVERY group of continuous text.
Thread the isolated arched paths together.
Do this over and over until all text now follows a circular arch matching your pie chart.
Here's what one group of continuous text would look like:
(text paths colored for clarity)
It'll take a while but the end-result will be much nicer.
Question is - will it be worth the time required, and the added headache if you have to shuffle the pie chart "slices" around if the chart changes?
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*EDIT
After looking closer at your attached image, I realized you're already doing what I've suggested.
Though, I don't know why the text in the light blue section is overlapping other text.