I was doing something similar for some chess boards I was making. I took a scrap piece of pine and hollowed out 6 squares (using dogbone corners) the exact size of the blocks I was cutting on. This also levels out all the blocks so they are the same height. Using the same .crv file, I then put the design I wanted to cut into the center of the square so I knew everything would be lined up. I ran into some issues with the blocks having a little wiggle to them so ended up using the masking tape/CA glue method of holding down.
I really like the solution that was done in the video Haldor posted and would probably modify what I did to use clamps that were marked so I could cut more than 1 at a time. Those straight line clamps good pretty good, too.