Well, maybe I saved this one. I took the cheese out of the brine and scraped off the slime with the back of my curd knife. After adding the CaCl the cheese has been in the brine for about 18 hours and it has stopped "melting." I've read most of the threads on feta "slime" here and next time I'll follow the advice of using the whey to make the brine. Intuitively, it seems that the whey would have a higher calcium content without modification and, with a PH meter, maintaining the correct PH is easily adjusted.
I'm wondering if using the whey the PH can become too acid and, if so, how would that be corrected?
I'll report on the outcome in another 48 hours of brining.