Minimum Number of Flips to Make Binary Grid Palindromic II

Given an m×n binary grid, flip the minimum number of cells so every row and column is palindromic and the total number of 1s is divisible by 4. The core challenge is to minimize flips by independently resolving each symmetry orbit of up to four mirrored cells (under row/column reversal) while satisfying the global ones-count modulo-4 constraint.