It does not take weeks if one uses a viable bacterial product. It does not require more than one addition of bacteria to work. And finally, you can stock a tank fully after using a viable bacterial starter to cycle a tank. I have only ever used Dr. Tim's and I mostly use it to get my bio-farm up and running. I rarely cycle tanks any more, I cycle filters. I can cycle filters for 8 or more tanks so I can stock those tanks heavily in about two weeks. If I were cycling a single tank it could take less time.
However, what tells me API is not thr right product is one simple line. But it also requires one know that the ammonia bacteria in salt water tanks and fresh water are not the same.
However, I have had 20 or more tanks running now for the past 20 years. So if all I need to do is to cycle a tank of 50 gallons or less, I simply seed the tank with bacteria by rinsing out bio-media from other tanks in the new tank. I may accelerate things by moving in a few plants. However, when setting up summer tanks, or preparing filters and tanks to take to a weekend fish event where I am either selling from my hotel room or in the vendor room, I need cycled filters and then up goes the bio-farm.
Um- how much nitrate is Sky high? I do not have sky high listed on any of my test vials or color cards. But, 1 ppm of ammonia-N can create a maximum of about 3.28 ppm of nitrite and 4.42 ppm of nitrate. Normally evaporation and any live plants or algae present will lower all of the these numbers. So with 25 ppm of nitrate in your tap and the max that the 1 ppm of ammonia you added could create, you should not have seen nitrate over about 30ppm.
I can also tell you the nitrate kit is the least accurate of all of our kits. Testing nitrate is difficult, so the way the hobby kits work is that they turn the nitrate into nitrite and then they measure that. If one is cycling a tank and has nitrite present, you need to test the nitrite and subtract that number from the nitrate result. If you have a 2 reagent test for nitrate, the 2nd bottle tends to precipitate solids out of the solution.
Before using it you need to shake it hard and then bang it on a table top and shake it again. Failure to do so can result in bad results. It is better to over shake and over bang the bottle to be sure it is mixed than to fail to get it well mixed. This will produce the most accurate results with a somewhat inaccurate test.
Nest, most kits come with an expiration date on them, check yours. And when buying at a store or online, check the date before buying in the store and on arrival from online. If the bottle doesn't last for some time until the expiration date, do not buy it from the store and send it back to the online seller.
Also, to increase your general knowledge about what is going on in your tank, I suggest you read here
https://fins.actwin.com/mirror/begin-chem.html It is easy to understand and will give you a bit more understanding about what is going on. However, it was written a while back and a couple of things are off the mark, but nothing serious.
Also, to come up with potential solution for you tap nitrate knowing the GH nad KH as well as the PH matters.
I still think you had the tank cycled and then managed to uncycle it some. The fact that your tank appears to have processed all of the ammonia plus some amount of the nitrite would suggest you are about midway through getting it fully cycled. But this also assumes you get a new nitrate kit and it shows your numbers are actually lower than your current kit claims.