So far I have dismantled six pallets, cut the wood into pieces which range from 10" to 19" in length about 1 1/2" wide and are approximately 1/2" thick. My goal is to laminate these pieces together.

I would like the wood to be put together on the flat sides (not sure of the correct terminology). I would also like the pieces to be randomly alternating in length. See picture below:

This will end up being a surface 5' long and 15" deep, for the surface of a media unit. My plan was to basically put them on a flat surface, glue them up and clamp them together. Obviously this is a rough idea and I am looking for some advice before I glue myself to the floor.

As a side note, this wood is for the most part straight and square, I have put each piece through a planer enough to remove about 1/4" of material in total from both sides.