You can fill the cells in the table (on your first screenshot) with 1 and 0. Then just load it into the array with AJAX instead of doing a bunch of "set value" actions.
And I agree with R0J0, making checkers game in C3 with an array won't be fun. I would probably use sprites with instance variables to store their position on the board, and overlapping checks to test if they can move to a certain cell.