Ion exchange sites in the peat moss will capture calcium and magnesium, thus bringing down your total dissolved solids. The latest thinking is that lower electrical conductivity (i.e. fewer electrolytes) is what "soft water" spawners need. So adding phosphates or other buffers, to stabilize the pH is counter-productive.
Eventually (or quite soon, if your water is hard) most of the available ion-exchange sites have taken up Ca and Mg, releasing that H+ that makes the peatwater more acidic. Then the peat is "spent." Don't throw it out, it's excellent soil conditioner for any kind of gardening.
Dry peat just won't get wet and just won't sink. So, pour a kettle of boiling water on it first, which will wet it and make it manageable. This is a good trick for peat going into potting mix or window boxes too. The hot water will make a "peat tea" that is perfectly good in the aquarium, but remember it's depleted of oxygen. Go easy!
(Guess I better look over the peat filtration section and make it clearer!)