Interesting approach. My first thought was to do what Vigo suggested with the dried cherries. I think I'll try taking about a 1/8 cup of dried cherries and getting some very hot water (not boiling though) and soaking them for 20 minutes or so. Blend that together to break them up and pouring that mix into the rest of the recipe.
I haven't been able to make that work yet. Part of my challenge is I hate sauces with any sort of solids. Anything I put in has to end up soft enough that I can completely liquify it during the process. I did try it once with regular ripe cherries and I was so slow at pitting them that I mostly failed. Maybe I'll try again by just cutting them in half and then straining out the solids.
Keep in mind that you're going to reduce a good sauce to something like 20% of the original volume of liquid. 1/8 cup isn't going to do anything. Think more like 3 cups if you want to try making an extract. I haven't tried that approach so I'm not sure exactly how much reduction extract you'd get out of a given amount dried cherries.
The cherry sauce I want is a sour one. Sour cherries seem to be stupidly hard to find here. In fact any cherries are expensive. I have considered ordering a restaurant supply size can of sour cherries as well.
Ironically I have a big cherry tree in my front yard but it's not a fruit bearing cherry tree.