trilogy problems, you are making this far more complicated than it needs to be. If you want to only add chlorine once a week, then you can do what some pool services do and have a high CYA level of around 100 ppm and shock up to around 14 ppm FC and then the following week the chlorine will likely be down to around 4 ppm FC if you are in a hot sunny desert area at which point you raise it to 14 ppm again. If you use only chlorinating liquid or bleach or lithium hypochlorite for this purpose, then to prevent the large pH swings you should have 50 ppm Borates in the pool. At least by using hypochlorite sources of chlorine you won't be raising the CYA level and by having a fairly high (but not too high) CYA level you will have relatively low chlorine loss from sunlight.

For a fuller technical discussion on many different chemical topics related to pool water chemistry, I suggest you read Certified Pool Operator (CPO) training -- What is not taught including the many links to more detailed scientific references.