After much discussion, we've decided to exchange water. We drained almost 1/2 the pool and are now refilling. We just didn't want to stay in the high-CYA/high-chlorine cycle! Hopefully, this will be enough to bring the CYA down to an acceptable level.
Any wisdom you can share about the steps I need to be thinking about while it's filling and/or just after it's done? Or, shall I look at some of the threads dealing with having a "brand new pool"?