What are some smart healthy ways to work with sour yet ripe blueberries and raspberries that does not involve a ton of added sugar?

Cooking berries, even a little, mellows their acid. You can easily make a compote or a quick jam by placing them in a sauce pan, fitted with a tight fitting lid, and a dash of sugar or honey or a sweetener of your choice, and place over the lowest possible heat. In about 10 - 15 minutes you'll see that they've relaxed, released their natural juices, mellowed, sweetened, and, best yet - concentrated in flavor. Once berries are cooked, even a little, they keep longer, and can be used in countless recipes! I like my berries on the sour side, in fact, because I find they can be quite flat if all they taste of is "sweet."

Make a fruit-infused vinegar, http://www.thekitchn.com/early-fall-project-make-fruit-129567

I’d make a cold fruit soup--maybe combine the blueberries with another sweet fruit--peaches?--to avoid adding too much sugar.

I would probably add them to my morning smoothies. Another option is to mix them in with some more sweet fruits for pie/crostata fillings. Scones could also work (I don't like my scones to be too sweet).