I am just reading this thread and nodding my head up and down. I have nothing to add. The line of questioning here is right on course.
Ok, maybe I have something to add. Even if the temperature has been high for an extended period, the addition of Calcium chloride could have increased calcium levels to cause a precipitation, especially given that calcium precipitates more readily at higher temperatures. (Wake - this is new to me. I believe you, but do you have a link? Knowledge is power!)
However, if you did in fact precipitate calcium, I believe it would have been visible. I have seen this occur in person, and it is very difficult to mistake for anything else. It literally looks like it is snowing inside the aquarium, unless of course it is just a small isolated precipitate on the heater.
Also, by testing pH in the evening, you are getting a higher reading than you would have received in the morning. This worries me, because your pH had a low point of below 7.8. I'm glad you caught this and are dosing accordingly.
Great questions on borate and magnesium. Some research is needed on this (google?), because if these concentrations are higher than the natural ratios in seawater, then the alkalinity test kit will give you a false low reading, with the result based on the assumption that magnesium, borate, and calcium are in balance, and the test actually testing for calcium buffering ions. So, if Calcium is 440 ppm and the other levels are unnaturally high, then calcium is more likely to precipitate, causing the rapid pH drop.
Fun stuff. Ironically, many sea salts add additional borate and magnesium for additional buffering capacity, on the assumption that the fishkeeper will not test for alkalinity as they should. The additional buffering helps between water changes.