I’m guessing not the Moody Blues. They didn’t do a lot of long instrumental sequences in their recordings, and even back when I was a major Moodies fan, the only one I’d have considered memorable enough to play even as a ‘deep track’ sort of thing would have been “Beyond” off the To Our Children’s Children’s Children album. And it isn’t anything like your description.
Since this was a classic rock station, all the OP has to do is keep listening for a couple of days and he’s bound to hear it several more times (with identification by the DJ).
Occasionally classic rock stations have some periods where they play deeper cuts and stuff, like Sunday afternoons or something.
But you can bet it’s a well-known band like the Moodies, or ELO, or something like that.
It’s not about to be some unknown entity, although frankly I’m struggling with acoustic guitar and violins with no percussion. I can think of horns, and organ, and electric guitar and a whole bunch of stuff together, but violins and acoustic guitar on classical rock confounds me.