Very strange... There's gotta be something in your tank that's generating nitrates on top of your stock. Two separate test kits reading the same thing and your tap reading as zero is too many data points to suggest otherwise.
I'd check the filter as recommended by your LFS then. Rinse the biomedia in dechlorinated water to make sure there's no gunk build-up, replace (not just rinse) the sponges and all around give the filter a good scrubbing and rinsing with dechlorinated water. It also may be a good idea to recharge the purigen too just to be on the safe side. That should remove anything that could be turning your filter into a nitrate factory.
Once that's all done, do your large water change and test the water. Keep changing the water until the nitrate levels start dropping. With 0 nitrate tap water it WILL drop once you change enough water. Once you've got the nitrates down the freshly recharged purigen and cleaned filter SHOULD keep it that way until they get gunked out again.