By the way, the pool store's advice to use an oxidizer is a bit ridiculous since chlorine IS an oxidizer! Using a non-chlorine shock (MPS) is going to be a lot more expensive than using bleach or chlorinating liquid and won't be any better.

You can take a bucket of pool water and add 6% bleach to it. 1/4 teaspoon of 6% bleach in 2 gallons is 10 ppm Free Chlorine (FC). You can then estimate how much chlorine it will take for your pool before it starts to hold. You may decide that's it is better to do a partial drain/refill than just adding chlorine.

Recognize that the DPD chlorine test will bleach out above 10 ppm FC making you think you have no chlorine when you actually have high chlorine. That's why we recommend the Taylor K-2006 that has a FAS-DPD chlorine test that won't bleach out (you at least get a flash of pink and can add more DPD powder) and can measure high chlorine levels accurately.

Though usually the CYA will get to zero when bacteria convert it to ammonia, it doesn't always go completely that way (other nutrients may run out or the bacteria just stop for whatever reason). You can read about my own experience with this and how I fixed it using chlorine alone in this thread.