AmE just solution/gist in time

The American English of my childhood had two different pronounciations
for "just" with different meanings. I can't find the distinction in a
quick look at a couple of dictionaries. Does it have a known
geographic distribution? Is there anything interesting to be said
about its origin or history?

In Kansas of fifty years ago, if I remember correctly, the "just" in
"just a minute" or "just right" sounded like "gist," whereas the
"just" in "a just solution" rhymed with "must." Pronouncing the first
to rhyme with "must" would have been bookish, although making the
distinction was part of learning to read, and pronoucing it like
"jest" would have been countrified.
.

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