peat lowers pH by reducing the hardness. I believe how it works is that the organic compounds in peat chelate (or bind) to the ions like Ca++ and Mg++ in the water and remove them, lowering the gH and therefore allowing the pH to drop.
Are you testing your pH from the tank, or from the tap? Are you allowing it to sit out for 12-24 hours before testing the tap water?
GH is not related to pH. Removing Ca++ and Mg++ will not lower pH. It's the bicarbonate (KH) you need to remove, and peat moss does this by the tannic acid reacting with the bicarbonate. The softening and acidifying actions of peat are separate.