You are bogging yourself down with all these tests. The readings you are getting make no sense. There is no way the water has a diff alk reading from different parts of the tank. Did it take the entire last drop of reagent to get to the endpoint color, or would 1/4 of a drop been enough? You are reading your tests in dKH, but how about meq/l? Can you tell if your at 3.9 meq/l or 4.1 meq/l? Do you see my point? Don't get so wrapped up in testing.
Your alk is rising, yet calcium is dropping. If the sand, as you suspect, was causing the rise in alk, it would also raise calcium. IO typically runs about 360-380 calcium.
I'm not sure what brand test kits you are using, but I highly recommend Salifert. Very easy to use and very accurate.
Also, please read the article I liked to earlier. ;)