I don't like their reading of zero for nitrate. It is very rare to have zero nitrate in tapwater in the UK - your tapwater reading is the lowest your tank should be unless you have so many plants they are using it all - but in that case your ammonia should be zero as well as plants prefer that as food over nitrate. Plants don't use nitrite though.
The theory of fishless cycling is:
You add ammonia and wait for enough ammonia eaters to grow to use the ammonia and turn it into nitrite. Once they start growing, the ammonia level drops and the nitrite reading goes up. Then you have to wait for the nitrite eaters to grow. This takes longer than the ammonia eaters did. The old method of fishless cycling said that every time the ammonia level dropped, you added more to feed the ammonia eaters (everyone used to believe they starved if not fed every 24 hours) but this caused the nitrite level to get so high the cycle stalled because the nitrite eaters won't grow at high nitrite levels - once the tank is cycled and has fish there will only ever be trace amounts of nitrite as the bacteria will eat it as fast as it's made.
We now know that the ammonia eaters won't starve if they aren't fed every 24 hours but we still do need to give them some food. The new method is designed to keep the amount of added ammonia to a minimum to stop the nitrite level ever getting high enough to stall the cycle. So we add a dose of ammonia at the start and wait till the ammonia level drops low then a second dose. After that, we wait till ammonia drops to zero with a nitrite of over 1 and add a smaller dose. And keep on doing this, adding a small dose every 4th day until the nitrite reading drops below 1, together with an ammonia reading below 0.25. Once this stage has been reached, a third large dose of ammonia is added and hopefully both readings are zero after 24 hours.
Your problem seems to be that your ammonia doesn't drop below 1 though you have zero for nitrite. The question is, is your nitrite zero because you have as many nitrite eaters as necessary to eat all the ammonia your few ammonia eaters are making, or is it zero because the ammonia eaters aren't doing anything and not making any nitrite.
If you add enough ammonia to get the level to 3ppm then monitor both ammonia and nitrite every 12 hours, this should show a few things.
If the ammonia does drop, we know you have some ammonia eaters.
If the ammonia level drops, you see a blip in nitrite and then that too drops, we know you have some nitrite eaters.
If your ammonia never drops below 0.5 to 1 but your nitrite drops to zero, there is something odd going on. I know that so many people say they have never seen a zero colour for ammonia even with tanks that have been running for years, but it is usually the 0.25 colour they see. Is it just that you are seeing an extreme version of this?
Could you do a couple more tests, please? Test both your tap water and your tank water for nitrAte; do it at the same time so you can compare the colours of the two tubes to each other rather than the test card. Are they the same colour or is one a more reddish orange than the other?
If the tank is redder that the tap test, you are making nitrate. If they are the same, you are not making nitrate. If the tap colour is darker, you are not making nitrate and the plants are using some nitrate that got into the tank when you first filled it up.