Well, with 1.0 ammonia in the tap, in the UK, I'd get onto the water board, as the legal limit 6months ago when my dad tested water for the Environment Agency was 0.5..... Things may have changed, or your kit could be giving a false high, but a complaint will get someone out to check and they have to do something about it if the reading is true. Hobby kits can be off though....
For the moment you are waterchangeing to remove ammonia. If your ammonia reading in the tank is higher than that of the tap, then waterchange. If the tank level is less than the tap, don't
Untill nitrite sets in anyway....
When nitrite begins to spike, you will have to ballence risks a bit. Waterchanging will short-term increase ammonia, but may save your fishes life if nitrite is up. If nitrite is above say 0.5, waterchange. Unless nitrite gets above about 1, I'd avoid waterchanges of more than about 50%. If nitrite is less arround 0.5-1 stick to 25%. Less than 0.5, leave it be...
Marine Aquarium Salt will reduce nitrite's toxidity, and may be worth considering here. Dose to 5ppm (or 1tbs per gal) while cycling, but discontinue used once cycled. For long-term use, salt can be dangerous, but for short-term use it is OK in some cases....
Try to avoid large routien waterchanges with ammonia in the replacement water. Aim for say two 20%'s a week instead of the weekly 30% for example to avoid raising ammonia too much. A cycled filter will remove the added ammonia with-in the hour without problems
HTH
Rabbut