What are you doing making a rear wheel drive civic or something? The CRV rear end wouldn't work very good. It's not a true RWD. Nor is it a true AWD.
It works more like a old suburu. It's a pump system that locks the wheel when it slips by using fluid pressure driven by an internal pump. You would be best off by using a true honda RWD. NSX, S2K is what I'd use but it's costly as you already know.