First, there was some melancolic acoustic guitar picking and a light, haunting female vocal. Think less whispery Belinda Kordic/the vocals of Worm Ouroboros. I caught these parts and wrote them down, but googling bits didn't bring anything up:

Drifting voices but my skin is on fire (something like that)

And you’re not listening anymore

The dogs are barking but the caravan’s leaving town

Here beside me

As a second falls apart

Disengaged, longing for their life

 

Not alive in a moment

Not alive in a moment

Not alive that moment (These three lines seemed to be the chorus)

 

Drifting voices and my voice is on fire

But you’re not with me anymore

I hope you got something from what you did 

From what you did

From what you have done

Male vocalist: Daddy, take my hand

Then there was a pretty distorted guitar solo backed by an insisting, monotone drumming, before it returned to the former mood and...

... the same male vocalist, but in French. As said, I'm not sure if these are all the same piece or just the radio channel fading between songs, but they all sounded like the same band.

So, if this seems recogniseable to you, I'd love to hear which band I'm missing out on.

Seems like a reasonable request to me - in what way is it spam?

Just found out the show could be streamed after the original airing as well, and this time managed to hear that the piece was Mostly Autumn - Dressed in Voices. It's a recent release, which explains the lack of Google hits for the lyrics. Case solved.

EDIT: not sure if the French and following parts was them too, though.

I know this is the internet and it's easy to suspect users with 25 posts, but I hate missing out on good music and the question was indeed "real"