yeah, StressZyme and almost every other bacterial additive contains the wrong kind of bacteria. They might initially eat some ammonia, but will die soon after and even contribute to ammonia in that way. The only bacteria you can buy that I know to be the right species is BioSpira. It's pricey, though, at $15-20 for one ounce, or enough to treat 15 to 30 gallons. Also, it must be refridgerated during storage, otherwise the bacteria will eat up all their food reserves and die in the package. That's another reason why bacteria in a bottle don't work. They have no food supply and are sitting on a warm shelf, with their metabolisms going full speed.
Keep in mind, also, that the nitrifying bacteria (the ones that eat ammonia and nitrite) in your filter and tank cannot survive without a food source. So without fish or adding ammonia from a bottle, they will starve. So maybe using filter squeezings days before you added the betta did not do much.
The tap water conditioners that detoxify ammonia do so by changing toxic ammonia (NH3) into the less toxic ammonium ion (NH4+). The two forms exist in equilibrium in a tank (i.e. both are present in different proportions, depending on pH and temp). Most ammonia tests cannot distinguish between the two, and read only total ammonia concentration. The only test I know of that reads only toxic ammonia is Seachem. Salicylate reagant ammonia tests are the ones that only pick up NH3, but Seachem is the only brand I know of (so far) that uses these.
I have heard people say that two-reagant (two different drops that you need to add to the water being tested) tests are salicylate. But I have several ammonia tests with two, even three reagant bottles and all say they read total ammonia. The ones I've used are Aquarium Pharmaceuticals, Red Sea, and Wardley.
Sorry, I know it's a lot of information. Anyway, I'd say ditch the StressZyme, keep using the water conditioners that detoxify ammonia, and possibly get some BioSpira if you think it's worth the investment. Also keep up with water changes. You don't need to gravel vacuum every time, especially if you'll be changing water every day or so. Sucking water off the top is quicker and less stressful on the fish. Just make sure to vacuum the substrate at least once a week, to prevent the waste particles from rotting and producing even more ammonia.
I hope that helps instead of confusing you!