There isn't any need to keep the pump running 24/7. You do want it on for several hours after adding the sequestrant to make sure the sequestrant mixes in throughly, but other than that the pump run time is not critical.
The next step, after lowering CH with the partial drain and refill, is to lower TA down to around 60-70. This is done by bringing PH down to 7.0-7.2 with muriatic acid and then aerating the pool. The acid will lower both PH and TA while the aeration will raise PH without changing TA. When the PH gets back up to 7.8-8.0 you repeat the cycle. It may take a couple of cycles of this to get TA down to the right level. You can aerate with spa jets, a fountain, pointing a return up so it breaks the surface, an air compressor, rain, kids splashing, etc.
Once you have done that you simply hold the PH around 7.0-7.2 and brush the stains regularly. This approach can be fairly slow, it takes days to weeks, but is reasonably safe and comparatively simple. You know when you are done by watching the stains, which should show visible progress well before they go away completely.