Update...
Still feeding the chlorine demand. 5# of dichlor and 39 gal. of bleach (or about 162ppm of chlorine) so far. Just got back from a week long vacation, and things are no worse than when we left. I had our friend who watched our dog dump in partial doses (1-2 gal of bleach per day) while we were gone. FC last night was 5.0 and CC was 18.5. I will continue to chlorinate. Hopefully we are nearing the end. We would like to swim this summer. :-/
(I decided not to waste my time/reagents on the bucket test. The results don't change anything. It will be done when it's done.)