DIAGNOSIS The meter is accurate for dissolved solids, but taste is affected by volatile organic compounds (VOCs) and chlorine. The carbon filter layer may be exhausted for taste even while ion-exchange works.
FIX Replace the filter. The activated carbon that removes taste and odor chemicals depletes before the resin that removes ions. A 000 reading with bad taste means the filter is partially spent.
IF THAT DIDN'T WORK Your water source may have high levels of non-ionic contaminants like certain sulfur compounds. Consider having your water tested for specific taste-causing agents.
HEADS UP Store filtered water in the fridge in a covered container. At room temperature in an open pitcher, it can absorb odors from the air and taste flat.