How does the water look? Still clear? No stains?
Did you happen to test pH when the FC was below 10 yesterday?
Sounds like you are on the right track. The only chlorine demand I recall like this was caused by ammonia that was the result of bacterial conversion of CYA over winter. Maybe your pool got into this situation, the bacteria could grow unseen turning CYA into ammonia if the active chlorine was low enough. I would, however, expect to see visible algae if the chlorine / CYA ratio was so low. Maybe it was the fertilizer.
Does the pool water stink of chlorine like a heavily used indoor pool (after the cover's been open a while) or does it have little smell?
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