I think you're having trouble because you are trying to find a math formula for using half square triangles to make a quarter square triangle square. The two don't easily mix.
I think what you should do is use quarter square triangles. Take two squares that are 7 3/4" square - one of each fabric. Cut them diagonally twice. This will still give you the 4 7/8" triangles, but the bias edges will be in the right place. I used 7 3/4" because it's 6 1/2" plus the extra 1 1/4" you add as per the standard formula for quarter square triangles. Your center block will finish at 6 1/2" which is just a smidge larger than the 6.45" that your center should be, based on a 12" corn & beans block.
Does that make sense?