Have you researched the origins of the log cabin quilt? I always find quilt origins fascinating :) Traditionally . . .the center square was red as that was symbolic of the flames in the log cabin's hearth/fireplace. But as my grandmother always said . . ."know the rules, then break away" :)
In order for your logs to stand out . . you'll want to add some contrasting fabric . . . .so you might still be able to make it work using your lovely batiks :)