Your combine chlorine levels are 15ppm? That seems REALLY high?
Your test results being that different really seem to suggest error in the testing. If you are running your pump, then replacing water shouldn't matter. That pool should be plenty mixed even just running the pump a few hours per day.
It's recommended to gather the sample water at several sites from the pool, from a depth of about 12 inches. But again... if your running the pump on a regular basis the water should be mixed very well. Replacing water or not.
Run the CH test on some water out of your hose. If the water is turning blue almost instantly, then you have 0 CH.
I am not familiar with your heat pump, but some pool heaters do require some level of CH and water can be "frothy" with
very little hardness.
Pick up a 50 pound bucket of Cal-Hypo 73%. You can get them online for about $100 shipped. Sometimes less. Use that to
chlorinate your pool for a while. One of the cheapest forms of chlorine you can get, and as a bonus has the calcium in it that
you want. So you get that "for free" too. Use it until your CH levels are where you want them. Then go back to bleach.
Mine CH levels are about 220-250 right now. I have a vinyl liner and no heater. I don't worry about getting them any higher.
You can probably go as high as 300-400 without having any ill effects or worries.