If you want to preload 6 adjecent tiles as suggested instead of 8, it seems better to make them hexagon-shaped as well (to make the distance to edges more uniform in all directions). I haven't implemented hexagonal tiles of vector data though - any experiences?
On the other hand, if the tile size is relatively small and you preload multiple tiles in all directions anyway, the proportional advantage of using Half Tile Offset or hexagonal tiles diminishes and code complexity prevails. (The scaling table in the end of the original article fails to distinguish that you don't have to preload all (2N+1)^2 square tiles either: you can approximate a circle with small squares and preload just about PI/4*(2N+1)^2 tiles ie. 21.5% savings.)
But then you incur the artistic complexity of hexagonal tiles....
So when Spidey was speeding up to some direction, I think it was three bricks that would start asynchronously loading, and others would get cancelled (say CancelIoEx on Windows/etc.)