There’s an easy way to glue up chess boards without dealing with all those little squares.
Say you want 1" squares. Start by cutting four 1 x 8.25" strips out of each color. Glue them together, alternating colors. Use a couple of bar clamps to hold them tight. Once dry cut 1 x 8" strips perpendicular to the original cut. Flip every other strip, glue up and clamp.
I made a board this way in high school wood shop out of maple and mahogany. I started to turn the pieces on the lathe but the semester ended. I still have the board but the incomplete pieces are long gone.
I like the idea of the floating board. It turned out great.