Write a function to solve an array or string optimization problem, demonstrating clean handling of edge cases and computational complexity.
Implement def max_absolute_product(nums): to return the largest absolute value of the product of any non-empty contiguous subarray. The input is a non-empty list of integers, and the output is a non-negative integer. Account for zeros, negative values, single-element arrays, and products that exceed the value of any individual element.
def max_absolute_product(nums):