What an interesting find!
Several sources mention that Steiner moved with his family to Mexico in 1958 to be the manager of "an independent recording company", though none of the ones I found specifies its name.
The sources differ slightly in how they phrase it, but as far as I understand it, the recording company he was working for was commissioned to create a music library (or was directly launched solely as a music library), for use either in Mexican TV productions and/or by the Mexican government in their documentaries.
- I guess it could also be an established 'independent' record company that branched out, launched a new division or similar, for this specific task.
Steiner, with his experience writing for radio and television (as well as for feature films), and I would guess, his involvement with the CBS' own music library, would surely have been a well-suited candidate.
It's unclear if Steiner wrote music for the library himself, or just managed it. One source mentions that he seems to have spent this period of security in a stable position, devoting himself to more 'serious' works, "including a cello sonata, a string trio and a woodwind quintet".
I'd say the timing gives us some good hints, however, even if the details are otherwise a bit scant; looking at the history, in 1958, Mexico had three commercial television channels (Channel 4, Channel 2 and Channel 5), with a fourth channel, Canal Once ('Channel 11') operated by the public University IPN, launching in 1959 (its planning starting a few years earlier). As this was government-funded, it seems a likely candidate - and the timing checks out too.
It's not that uncommon for television networks to have their 'own' music library (this was the origin for several of the UK libraries, for instance), but it unfortunately may also have been purely in-house, and never distributed outside the networks' own productions.
I'll do some more digging and see if I can find anything more concrete.
edit: Oddly, I found no related copyright entries for this period (1958-1961) attached to any Mexican company.
However, Television Academy Foundation's excellent "The Interviews: An Oral History of Television" series, did a lengthy interview with Fred Steiner before his passing, where he recounts his stint in Mexico quite differently, and mentions scoring a few films/documentaries for the Mexican government, as well as music for commercials - but nothing about any independent record company or its associated music library - though it is clear he was no longer working for CBS at this time due to a falling out with its music director Lud Gluskin. He does, however, mention that there was some recording activity in Mexico around this time due to union complications in the US. Also, directly contrasting the anecdote about 'serious' works above, he outright states that he could never have made much of a living in Mexico.
https://interviews.televisionacademy.com/interviews/fred-steiner - see Chapter 5.
Telling a slightly different story entirely, IMDb's bio of Steiner (penned by one of its users, I think?) claims that he spent his time in Mexico "compiling and archiving Latin American music for government-sponsored television documentaries" - though where they got this from, I don't know.
edit 2: Found it!
A notice in the April 15th, 1959 edition of "Variety" gives us some more details:
So he served as 'consulting manager' of Mexico City-based company
Repertorio de Musica Grabada S.A.Its addresses:
Michelet 72, Col. Anzures, Mexico 5, D.F. / Tel.: 28-71-62
Av. Juarez 134, Desp. 306, Mexico 1, D.F. / Tel.: 46-27-56
Unfortunately, the trail seems to run cold here. I can barely find any mention of this company outside this magazine ad.
