If I'm not mistaken, the Recording came in this case . . .

The early ones till about 1954 yes.
However, for several years it also shared the same case with the Mendez trumpet/cornet . . .
No, but similar shape, never that color.
And, I believe both the Mendez and Recording were later available (late 60's) in the Samsonite style Olds case . . .

Only late 60s, early 70s
So, any of the above would be technically era-correct. And, in spite of its slightly different valve configuration, the recording should fit it any Olds trumpet case. Or for that matter,
any full-size trumpet case.
Any of the Recording gurus out there . . . please chime in to correct me.