Can one simply choose to craft a Shoddy version of an item?
I'm not aware of any rules saying that you can. Other than certain things that specify that you end up with a shoddy item by using them - such as the Junk Tinker feat that you mention.
That doesn't mean that you shouldn't be allowed to do it if you want to - just that there are no rules for it. So it is well into GM Fiat and Homebrew territory.