If all signs in the prison camp were written right-to-left instead of vertically, they probably would have noted that before creating the sign. Especially considering their lives depended on it.
One of these signs is written right to left:
https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcQdiwLY...
https://auctions.afimg.jp/h1085974646/ya/image/h1085974646.2...
Which one is it? There is no way to tell unless you already know the characters. Unless someone could read the existing signs they would almost certainly assume they were left-to-right and make any new sign like that if they only had the characters to copy.
Did you happen to see the lathe? I ask you, which would be more difficult to get right in the smallest detail?
While most Allied soldiers would not be literate in Japanese, that doesn't mean they would all be completely ignorant, either. It just takes one to know enough to ask about character order.
While I agree that it was high risk, I'm willing to believe the people who were present when they say they pulled it off. Sometimes we dodge bullets without even knowing they were fired.
Can we agree that it seems improbable that they fooled anybody about who drew the sign and also agree that they got to keep their workshop and their tools and have an amazing (and true) story?
I mean, consider this in the abstract - the objections you're making here rest on the implicit assumption that you know more about the realities of life in a Japanese POW camp than TFA's author. (After all, if he fabricated the story about the sign he'd obviously fabricate it so as to be consistent with his experiences in the camp.) Do you really think that premise is more likely than the alternative - that TFA's extremely brief telling of the story simply doesn't include whatever details would answer your objections?
The only premise the story depends on is: that the camp guards saw the workshop and took it for granted that it was approved by somebody, since it was orderly and operating openly. If you accept that, it doesn't matter if the sign was amateurish or even upside-down - it would just look like something the workers had been told to make, or had made themselves to test the tools or to pass the time.
A bunch of posters here seem to be imagining that the sign was the lone keystone of the ruse, and that for some reason it needed to look like it was written by a native speaker or else the whole plan toppled. But nothing in TFA suggests that, it just says the sign was one of several things the POWs did to make the whole setup look like it had approval to be there.