While not quite the Traveling Wilburys ... this is The Lost Dogs - Arguably the best anti-mainstream-Christian-music supergroup ever. From left - right Mike Roe (77s), Terry Scott Taylor (Daniel Amos, The Swirling Eddies), Derri Dougherty (The Choir), and Steve Hindalong on drums (The Choir). Play it Loud, play it often.
I started following these guys spereately in their respective bands way back in the early 80's. I was amazed when they joined forces and formed The Lost Dogs (so much talent). Don't be put off because they are a "Christian' band - so much really good music , definitely worth a listen. Also, so very hard to find decent live recordings/videos.
The Lost Dogs
Eleanor It's Raining Now
Bullet Train
Get Me Ready