Then, we have a precious little bit from a dialect:
feiDE - used in Bavarian dialects to amplify / emphasize a statement,
Nice idea to suggest "fei". I thought about it myself, but refrained from it, because it probably is a bit too exotic. It's hard enough to explain to German speakers, what this "fei" is used for, because - as you say - it is a word restricted to the southern part of Germany and isn't understood correctly (and of course not used) by other speakers.
You gave some examples, but the meaning can be summarized to a quite simple concept: You use "fei", when you make a statement, about which you think (or know), that your listener(s) don't know it, but MUST now it. It means, you use it in the sense of "Listen! What I tell you now, is most likely new to you, but I think, that you really should know it."
Take your examples:
A teacher overreacts and puts the whole class in detention, one of his colleagues might comment:
Das war fei nicht in OrdnungDE - that was really not right.
(= It seems to me, that you don't know, that your action was wrong, so I tell you, that it really was. You should know that.)
Person A says something, Person B (incorrectly) points out a mistake in Person A's statement. A third person might then comment
Das war fei schon richtigDE - but that was indeed correct.
(= It seems to me, that you don't know, that the statement of A was correct, so I tell you, that it really was. You should know that.)
If you see something very beautiful, you might say
Das ist fei schön!DE - (Oh my!) This is truly beautiful!
(= You maybe don't recognize, how beautiful this is, but you should! So I point this information out to you.)
You want to let someone know that there is an easier / better way to do something, or let them know that something is actually available to them (e.g. someone is using a hammer instead of a screwdriver):
In der Schublade ist fei ein SchraubendreherDE - FYI, there is a screwdriver in the drawer.
(= It seems to me, that you don't know, that we have got a screwdriver, but you should know it. So I point this fact out to you.)
The Japanese have a related partikel. They add "-yo" to the end of the sentence, to cover the meaning of "fei" quite well, e. g.
Kono tokei wa takai desu yo.
This clock TOP expansive is *yo*
You would e. g. use this sentence, if your friend makes not so nice comments about your clock, e. g. about it's cheep-looking design. To emphasize to him, that the clock is really expansive - a thing he obviously doesn't know, but SHOULD know (in your eyes) - you use "-yo". In the Bavarian dialect this is also a very good example for "fei":
"(Hör gefälligst auf zu lästern.) Die Uhr war fei teuer!" - (Stop mocking my clock!) It was *fei* expansive!
I'd like to see "fei" too in Na'vi, but thinking over my demotivating experiences of teaching this concept to other German speakers, I'm not quite sure, whether it will be understood and used appropriately by speakers of completely different languages. Maybe the Japanese Na'vi-learners will get it right.