You need to increase the pH and KH as that is likely low as well during the cycle. The bacteria need carbonate to grow and they grow better at high pH. The easiest way to do this during cycling is to add bicarbonate of soda, sold in the home baking section of the supermarket (not baking powder!) Add 1 tablespoon (15 ml spoon) for every 50 litres water, wait for it to mix and test the pH. If it is somewhere around 7, fine. If it is lower, add some more till it reaches 7. Keep an eye on the pH during the cycle and add more bicarb if it starts to fall.
Bicarb is not very good for fish so you will have to remove it once the cycle has finished. You have 2 choices.
Either remove as much water as possible after cycling has finished and try something like crushed coral or limestone or even coral sand as a substrate to boost your pH and KH. Or add remineralisation salts such as those used with RO water - though with this route you would need GH and KH testers as well, and at every water change check the new water before adding to the tank to make sure it is the same as the water already in the tank.
Or you could have the tank water at the low pH. There are plenty fish that would thrive at low pH eg most Amazon fish.
The way to do this is by doing several small water changes at the end of the cycle to slowly remove the bicarb and allow the pH and KH drop slowly giving the bacteria time to adjust. Keep dosing the one-third dose of ammonia every 2 day during this process, checking both ammonia and nitrite as well as pH. The theory is that a lot of bacteria will not survive the pH drop, but some will and they will multiply to replace the ones that die. After the pH has dropped to your 'normal' level you should have only bacteria that can cope with the low pH. Then add a full dose of ammonia to check and if you have double zeros the following day, do a big water change and get fish that like very soft, acidic water.