First of all, I think your idea is great, regardless of what they call it. It kind of reminds me of Chickenfoot with Sammy Hagar and Michael Anthony formerly of Van Halen, along with Joe Satriani & Chad Smith.
To get things started, it would be great if Felder were to invite Leadon & Meisner to join him on his tour with Styx to get the ball rolling, and see if they all enjoyed it. (This presumes of course Randy is up to it).
Heck if the Eagles are really done, invite Schmit & Walsh along as well as special guests.
Having Leadon, Felder & Walsh all on stage playing guitar together would be worth the price of admission.
Ditto for having the great vioces of Meisner and Schmit together as well.
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I have always felt "I Wish You Peace" was an underrated song.
Now I know according to Henley it was "not up to band standards", and they supposedly threw Bernie a bone to keep him happy.
The heck with that, it stands on it's own.
I suspect ( though I cannot know for certain), part of the issue was because it involved Patti Davis.
I know the mods here do not like discussion of politics, but the Eagles in the form or mainly Frey & especially Henley, allowed their personal politics to dictate a lot of decisions.
Had it not been for that fund raiser for ultra leftist Alan Cranston, maybe the band wouldn't have blown up the way it did. Or at least not as soon.
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As to Azoff, why would they want that little gnome to be involved?
I am not sure about how Leadon feels about him, but I know Felder & Meisner feel he torpedoed them in their solo careers, and looked out only for the interests of Frey/Henley above all else.
This potential group you propose would do well.
So get right on it!