I actually WAS able to open the crafting log while crafting at some point. I think it was when they first added the "view recipe in crafting log" thingie to the scrip turn in window, and I could then go through the crafting log by using that just to get it open. Unfortunately, it tended to cause some sort of glitch where you weren't able to interact with anything after finishing the recipe. I think they patched that glitch out a while ago though, so you probably won't be able to open it that way anymore.