Alternating the board grain will keep the sign from curving severely when/if it warps. The sign will become wavy instead, which is better because you will still be able to read the sign, but this is a worst case situation for wood warping. If used inside only, it shouldn't warp at all if finish is applied to seal on both sides and edges. The best choices of wood to minimize warping is wood with straight grain lines running across the narrow dimension of the wood. I have frequently bought wider boards and cut them to remove the center tightly curved pith area to get boards with the straighter across the board grain lines. Quarter sawn wood better achieves this when the boards are cut, but at greater material cost and difficulty to find. I have ripped construction lumber in 1 1/2" wide strips, then turned each strip 90 deg and glued it back together to get the grain the way that I wanted for better stability. This method made some great looking and stable 1 1/2 thick pine table tops that have remained flat for the past 30 + years.
My experience when trying to joint with a router involved using a piece of straight steel angle clamped to the board, positioned so as to remove about 1/16 of an inch of material with a straight bit and router running along the steel angle. We then turned the angle around and did the same for the opposite edge of the board, but this time we set the angle to be parallel with the first edge, and the result was boards with parallel and well jointed edges. It worked much better than I expected it to. I have a jointer in my shop, but used this method when away from my shop and helping a son with a project. I had a saw and router with me, but no jointer, so I came up with this method and it worked much better than I expected it to.
Central North Carolina