You have an interesting possibility there. Bororas brigittae, the chili rasbora, has a 20-28 temperature range. What would you get if you went with no heater? What are room temps like in your house?
I had a group of the related Bororas maculatus that actually bred quite a bit in a softwater tank at a room temperature of 21-22. So the CPDs are known to like the cooler side of their range, and the Bororas don't mind. I've never kept shrimp to know though.
There's no guarantee it would solve the fighting. But going for the lower safe range with a number of small fish has dialed down aggression here. The fish often live longer too.