"Off all smth."

Hello.
I would like to learn more about the use of the, as I define it, "off all + (adj.) + noun" construction like in "...in LA - off all places! - can you imagine this?.." (heard from a native speaker), meaning (sounds somewhat awkward but the meaning is all there at least) "it is such a strange coincidence that X happened in Y while there are so many other places more suitable/probable for this event to happen in/at". I would like to get a link to a dedicated source with a detailed and exhaustive explanation (of there is any). Thanks in advance.

What you heard was, "...of all places."

It is such an unlikely place to find this/to have this happen ( which implies that there are many other places where this would be a normal occurrence/finding, or of little surprise to the person.)

Can other posters recount some of their experiences, as examples of this for Quadratin?

''Of all the gin joints in all the towns in all the world, she walks into mine.'''

The last person Rick expected to walk into his bar in Casablanca was Ilsa (who he had last seen years before, in pre-War Paris): read more here - Casablanca (film) - Wikiquote

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Hello again and thanks for your guidance.

Now it's settled: no more learning English from stoned Australians whom I heard this from and who kept on assuring me that it's "off" not "of".
Well, he who searches finds... in my case it's "Gosh! Of all possible moments...". Is this a good one?

And here comes another "unrelated" question... Is everything ok with how I phrased the question that initiated this thread? I guess, there might be some mistakes using articles (not to mention more).

And to whom it may concern...
List of 18 Types of Subject/Verb Inversion
Any comments on this?
Nothing's wrong (in general)?

Thanks in advance.

Oh, dear! How fortunate you asked.

Quick and painless will be your medical procedure.

A better example might have been, "Slow and steady wins the race" and indicate that we don't use this in everyday speech, but as in this example, in adages.

Can others help to go through each of the inversions and tell which we use in daily life, which are literary expressions, and which should wither on the etymological vine.
(You might like to quote some of the examples given...for a laugh.)