Thanks to all who chimed in on the testing issue. I am indeed doing it overnight, after the sun leaves the pool in the evening, and before it hits the pool the next morning. My dipper is clean (get your minds out of the gutter).
I think the chlorine is not consistently mixed in well when I test. You see, in the midst of my algae eradication process, I ran the pump for 24 hours. This means that regardless of evening or morning test, the water was always being agitated. Once I resumed normal pump operation, the first evening test was with the pump running, and the subsequent morning test the pump had been off for hours. But, then I changed the time cycle of the pump, and while it is always on when I did the evening test a couple of hours after adding chlorine, the amount of time the pump was off prior to the morning test could very well be what's making the difference. Maybe there's scientific theory to contradict that, but what else could explain that, when my 24 hour loss tests that have always been performed when the pump's been running, are starting to yield more consistent results?
Before anyone gets their panties in a bunch over my last statement, accoring to what I have read (and everything on the internet is true), chlorine can separate from water. Combined with the fact that I have to run much more chlorine than the average CYA pool, and that I keep a cover on the pool, I think it's a good bet that when the pump is off for a considerable amount of time, there is bound to be different concentrations of chlorine in different areas of the pool.
I do not want to run my pump 12 hours to ensure proper mixture to span morning and night tests, so I'm going to stop obsessing about what the overnight loss really is. Regardless of my limited experience with the TFP method of balancing a pool, I think I've had a pool long enough to know when something is off simply by looking at it. Isn't that why God, or whoever you believe in, invented algae that survives in pools, and particulates like phosphates that cloudy waters; so we can easily see when something is amiss?

I will just monitor 24 hour periods for now to find my pool's nominal daily loss, and balance from there.
I wonder if my high CYA, and the subsqently higher amount of chlorine I must ensure is mixed into my pool, contributes to the inconsistent test issue. I will be checking with local my Water Nazis when I get back from my trip. Thank you, maniacalmama, for doing the initial leg work for me on that. Sine you're so good at things like that, when are you coming my to help with my daily dosing?

Oh, and for what it's worth, longer posts are more helpful than short ones sometimes. As you can tell by my posts, verbosity is king.
Regarding my question about when to run the pump, what I meant was, are there better times to run the pump to help with minimizing chlorine loss? For example, does running it during the daylight hours cause chlorine to be higher in the water column, or something, and thus more easily burned off, in which case it would better to be run the pump at night? Or, does mixing into the water help keep it from being burned off, thus be better for the pump to be run during the day? Or, does it even matter?