That doesn't reduce the number of cells touched, and would make the algorithm more complicated. It would also probably hurt cache locality. Going backwards is also pointless complication, you could just as easily cut into two sections and go forward in both.

And furthermore why split in two? Why not split the range into three sections, or four, or N and completely unroll the loop?

Probably not a good-tasting construct at all.

And what do you do with odd grid sizes?

Honestly the whole second half seemed damned weird. Give the requirement to zero the edges of a two dimensional array, it's so astonishingly obvious to just hard code the 0 and width-1/height-1 that do do anything else suggests a special effort to make a sub-optimal solution simply for arguments sake.