With some lobbying to the creator of little Golem, a place to play the Amazons Cross variant was finally created.
As you can see from the poor quality photo below, the game no longer starts with white's 4 amazons towards the bottom of the board with black's 4 amazons on the top portion. Now both players have equal access to all four corners of the board.
In my opinion the opening in this variant is much more entertaining and negates the first player move advantage in the traditional set up.