Copper precipitates when the pH rises as copper hydroxide and copper carbonate. The latter can be reduced by having a lower Total Alkalinity (TA). The former can only be reduced by having the pH be lower. Both can be avoided by maintaining a lower level of copper.
The metal sequestrants don't actually physically remove the copper, but bind to it such that it doesn't react with the hydroxide or carbonate, but such compounds do break down over time. Only physical dilution of the water with fill water that is lower in copper will reduce the actual copper concentration.
Also, realize that pH Up is Sodium Carbonate so raises both the pH and also the TA quite a bit. As you have noted, when the TA was low (as well as the pH) the water was clear. So next time you want to raise the pH don't use pH Up. Either use 20 Mule Team Borax (in roughly double the quantity as you would with pH Up) or try aerating the water. Borax will raise the pH with about half the rise in TA and won't add any carbonates to the water. The borates (boric acid in water) from Borax will also act as a pH buffer if you accumulate enough borates over time. Aeration will raise the pH with no rise in TA at all. There are many ways to add aeration to the pool, but one of them is this clever device
It sounds to me like your copper ionization system is set too high in terms of having too much copper in the water and also that you are using pH Up to raise the pH and end up raising the TA too much as a result.
I'm not sure what posts you've read that have concern for copper and low pH. I don't understand what the problem would be in that case. Low pH below 7.0 can become corrosive to metal, but it shouldn't be a problem for copper in the water. In fact, some chlorine-free systems such as EcoSmarte have high levels of copper and a pH close to 7.0 (I am not promoting such a system -- just using it as an example).
As for having a low chlorine pool, there are other ways to accomplish that without using copper. Bacteria and viruses are fairly easy to kill so only require very low chlorine levels. It's algae that is harder so using an algaecide such as PolyQuat 60 or a phosphate remover would then let you have a lower chlorine level. However, it's not the Free Chlorine (FC) that determines the actual disinfecting and oxidizing (hypochlorous acid) chlorine level but rather the ratio of FC to CYA that approximates this concentration. So you can easily have very low chlorine levels by having a lower FC/CYA ratio while still having enough chlorine "capacity" to oxidize bather waste (urea/ammonia from sweat, mostly) albeit more slowly. So long as you have the algaecide to prevent algae, you could have 1-2 ppm FC with 100 ppm CYA which would be technically equivalent to 0.3 - 0.6 ppm with 30 ppm CYA or 0.01 - 0.02 ppm FC with no CYA which is a very low level of chlorine.
It would be one thing if you wanted a chlorine-free pool and were set on that, but if your focus is on low-chlorine then you really do need to understand how FC and CYA work together. The idea that a higher FC means more exposure to "active" chlorine is just not true. I can tell you from my wife's personal experience that the CYA level makes a huge difference. Her swimsuits degrade in just one winter season of use in an indoor pool that has 2 ppm FC with no CYA in it. In our own outdoor pool during the summer with 3.5 ppm FC and 30 ppm CYA, her swimsuits last for multiple seasons with minimal degradation even after 4+ years. The difference is the factor of 20 difference in "active" chlorine level in these two situations. CYA acts as a chlorine buffer with most of the chlorine held in reserve and inactive so you can easily tune your chlorine concentration by adjusting the FC/CYA ratio.