I like to move to center gradually. First I bring the thickness down to 1/2" or so for a distance of 1/2" to 1" depending on my mood and the difficulty of that section of the wood. Then I take that down to 1/4" or less.
Gradually work in towards center.
Reducing the center "island" more
and more with each pass
until the center is reached and we are ready to sand.