Cutting grit BATT (assuming you use the new Pandemonium sticks) works well with a slow water drip, or even a spray bottle. I would recommend that you use 600 for fine cutting, and 3K for prepolish. You shouldn’t need the 1200.
nightrider has it right in emphasizing cleanliness. The toppers, however, are going to give you trouble no matter how clean you are. I wouldn’t use them for anything other than rough preforming. It is possible to use both sides of a BATT if you are careful. Some people use a throw-away coffee filter (with a hole for the spindle) under the lap to help prevent cross-contamination.