I've found that the number pad is very good for sweeping most common areas of the map - the beach, turtleshells, and tablets are all mostly inside one of the number-pad zooms. It's always my first step, before sweeping around by hand - and probably why feathers almost always are the last or second-to-last thing I complete.

Leo - my reccomendation would be to run TWO villages, side by side. Get them to fishing, and forget other considerations. Then just spend a certain amount of time in each one each day - that way you'll be sure it's not because you spent more time in one than in the other, or more time sweeping collectibles in a village that wasn't in danger.

Additionally, I'd be leery of trusting the results unless you repeated the test at least once, preferably twice with both villages - a random distribution is not an equal distibution. This means that using a different methodology, even if your chances are higher, does NOT guarantee that the pieces will appear faster. In any game, at any point, you might get lucky and get every tablet peice in the course of one hour; in another, you might not find a single one for months. This might occur even with all the circumstances exactly equal.