1.3 pounds of CYA in 5300 gallons should produce about 30 ppm CYA in the water. As Grace pointed out, it may not have fully dissolved, but I would have expected some sort of measurement on a CYA test -- but test strips may not be good for this sort of test. You should invest in a good test kit such as the one
here which is essentially a better balanced (in terms of chemical quantities) version of the Taylor K-2006 test kit found
here though it also has an OTO chlorine test as well for quick chlorine checks.
The Nature2 system is an expensive way to keep algae at bay and it will slowly kill bacteria, but chlorine disinfects much faster which is why it is required even when using Nature2. You should keep in mind that having even 4 ppm FC with 30 ppm CYA in the water is technically equivalent in disinfection and oxidizing power to having only 0.13 ppm FC with no CYA. If the reason you are using Nature2 is to keep chlorine levels low, then that is a false proposition. An outdoor pool exposed to sunlight and breezes and with CYA in it is extraordinarily safe with chlorine. All of the issues with asthma and respiratory problems with competitive swimmers and small children quoted on websites promoting alternative products for sanitation are ALL with indoor pools that do not use CYA, have poor air circulation, and no exposure to sunlight. Even at 2 ppm FC with no CYA in such pools, they have over 15 times as much disinfecting chlorine which results in 15 times the rate of production of disinfection by-products. The point is that YOUR pool, using CYA and 3-4 ppm FC, is far, far safer than the pools that have had problems with chlorine and no CYA.
As an alternative to Nature2, you might consider just using chlorine alone IF you are diligent about adding chlorine every day (or, if you get a pool cover, twice a week). If you feel you won't be able to maintain the chlorine level consistently, then you can use a weekly algaecide such as PolyQuat 60 that will prevent algae even if the chlorine drops to zero for a while, though clearly you shouldn't go into the water until chlorine is added and you wait several hours. Compare the price of PolyQuat 60 and the Nature2 to see what makes sense for you and also keep in mind that the copper from the Nature2 system can lead to green hair in blondes and to metal staining if the metal amount rises too high or the pH goes up too far.