I found one of these programmes on archive.org, and the song you are after is included in the closing titles.

https://archive.org/details/theroadtogettysburgcivilwarpart118611863

I can't find more editions of the programme. Archive.org is wonderful, but poorly indexed - I searched for "NBC exploring" to come up with the above, but if folk can think of other, more creative search terms they might well be able to discover further episodes.

Dave