Instead of clamping down, use them as a spreader. I do this when I need to separate a dovetail drawer and don't want to mar the wood with a hammer, or to open up chair legs to remove a spindle.

You can use a brush, a spreader, or even a scrap piece of wood for this. In this example, you will need to apply the glue to both sides of piece two. Stack the layers like a sandwich with piece ...