I may have figured out the problem. I restarted again, and during the "Transport 10 Dirty Copper Ore to the Smelter" mission, I observed that every time the Smelter would smelt the ore in to Copper Plates and consume the ore, the mission count would reset to the amount of ore still waiting to be smelted.
That suggests that the counter is not actually counting how many times you transport the goods, but only how much is currently in storage.
Thus, you have to do the tasks precisely as indicated without "jumping ahead". I.E., produce 10 Copper Cables, only then transport them to the Launch Pad, and only when they are all there, then Launch.
(If I do not post again after trying that, assume it is correct...)