I thought you were only going to have one layer on top with the holes and a solid colour underneath.
For more than one layer you could use a jig with dowels and just drop the glued strap on top of the first one, that way all the holes line up.
To punch through more than one layer, one complete strap at a time you could purchase the tubes and make your own punch from a block of wood or plastic, the only other option would be to have a shop make it for you.
If you purchased the tubes a machine shop would likely charge you a hundred bucks or so to lay out a block and mill it.
Another option would be a drill press, make your layout , center punch each + and then drill each one.