You can take a solid piece of wood cut to the size of each stack of lumber, and score horizontal dimensional lines. I use this method for making wood crates simulating individual boards. I made a jig using a scrap piece of 1/2" plastic sheathing with sharp pointed paneling nails spaced in a triangular formation with the points sticking up through the sheathing just enough to make fine score marks. I use a guide attached to the length of the plastic to keep the wood true through the jig while pushing it across the points. The triangular pattern is so the board doesn't make contact with all the points at the same time. The other reason is that the nails have to be spread out due to the closeness of the spacing. Dimensional lumber is 1.5" thick, which is about 1/32". Drill a pilot hole through the plastic using a bit just about the same diameter of the nail. or use one of the nails as a bit.
I use white pine, because it's readily available in the scrap bin in the school wood shop. Bass or balsa would be a better choice for new lumber. My crates simulate old weathered boxes that have been outside for a while. It also would be less noticeable that it was a solid bloc of wood, as there is no real grain.
It takes a while to get the jig made,because it has to be precise, but it saves a lot of time. I use plastic for the base because there is very little friction when pushing the board along. A little light sanding may be needed to remove any strings that may be produced. If the jig is spaced just right, it is only necessary to do one half of the lumber stack, as the board can be turned around and scored from the other side.
I have one of these cars, so at some point, I'm going to make a jig for it
I've included to pics of the crates as an example. The spacing is not consistent, as I wanted to replicate boards of different widths.
Don