Just dug into my archives a bit and had a root around for some info from way back...

Atlas Shrugged

Over perhaps all other unreleased songs this one seems the most mythical and desired and maybe that's  because we came so close to getting it. Axl confirmed in his chats on the forums in 2008 that the song dates back to 1999.
It was slated for release on Chinese Democracy but was removed at the 11th hour due to the time  constraints of the CD format. The earliest versions of this have Robin Fink on lead. Brian May recorded guitar on this at the same time as Catcher In The Rye and Riad & The Bedouins. It seems likely that Brian’s work was scrubbed in favor of Ron Thal’s given that’s what took place with Catcher In The Rye & Riad, Certainly Ron did record a solo for this song.

As of 2008 Axl however seemed at least open to the idea of an alternate version, when asked about the song on HTGTH he  responded...

"Perhaps on an alternate or bits, on that track it has more to do with recording issues and getting the  mix to a good level."
The idea of working with Brian was not necessarily born from a need to get the Chinese Democracy album released, but in fact had been a plan behind the scenes since the mid 90’s

“We may work with Brian May on a project upcoming. We get along with Brian really well." Axl Rockline  Radio 01-03-94

"I go back to listening to Queen -- you know, we're still hoping to have Brian May come in and do some  tracks, and I got a fax today that he's coming in." ( Axl 8th November 1999) 
http://www.heretodaygonetohell.com/arti … ticleid=28

"JANUARY 24th 2000 I hope you've all had a good weekend? It's all still pretty quiet here - Brian is back from working with Axl in Los Angeles on the new Chinese Democracy Guns n Roses album. I don't know yet what  tracks will feature Brian, I'll let you know when we know. Roger is down in Cornwall shooting (pheasants  apparently!) and John is at home. "from the official queen fan site: http://www.queenworld.com/

'Atlas Shrugged' is described as being somewhere between 70's glam rock and 'November Rain'. (Jeff Leeds,  Sp1at Website 2005)

"Song doesn't have all that much to do with the book other than trying to do what you believe in and a line  about shoulders not being wide enough". (Axl Rose, MyGnR Forum, Dec. 2008).

"'We were finishing track in October. 'Doing overdubs with Buckethead and Robin Finck and some stuff with Tommy Stinson. I felt we had a well finished version of The Blues, Madagascar, Chinese Democracy. Atlas Shrugged was pretty good.'" (Classic Rock, April 2008) Tom Zutaut

"Atlas Shrugged, I was going to tell a little story about that song. Right now on my laptop, I actually have  the old guitar solo that I played for that song, when, two days before the album was going to be mastered, I was like, let's see if we can squeeze it on to the album. I busted out some guitar tracks for it, I have my own studio... (Bumblefoot, Eat More Heat, March 2013)

What follows is an excerpt from Brian May's appearance on the BBC Radio 1 Rock Show...

“They just said come over and do  some stuff. It's a long story, to be honest, and I won't bore you with all the details. But Axl was feeling that he was in a difficult place because the guitarist he'd been working with on this new album had, sort of,  replaced Slash, because they fell out, sadly. I think that is sad actually because they're both brilliant  talents and great with each other. But the guitarist that'd done most of the tracks had departed and Axl  had a real emotional attachment to what he'd done, and yet he didn't want him on the album, I hope I'm  not saying too much here, he didn't really want him to stay on the album because he'd disappeared, you  know. So, he's sort of feeling a kind of divided loyalty and he said, 'Brian can you come and do stuff which I will like and I won't feel too bad about ditching this other stuff?'. So I did. I went over there and I think I  played on three tracks and messed around on various other things. But it worked out pretty well, as far  as I can tell. And it's very strange 'cause most of the Guns N' Roses people are not there 'cause Axl's
sacked 'em all. So you're talking about Axl and the 'new' Guns N' Roses but, boy, is there a lot of energy  there and his singing is outrageous. There's some great tracks on it. (Brian May Wed 10 May  2000). The presenter was Mary Anne Hobbs http://qfg2.info/gnrnews_old.html

The song finally leaked to the fanbase in 2019 with the versions detailed below, but this was not the first time traders had the song. According to Mick Wall in his unauthorized biography, Atlas shrugged was out there in private circulation. The book predates Bumble re-doing the solo, so if Mick Wall is correct then the version out there was the Brian May one. However it is more than likely an inferior quality version of a mix that leaked later.
If the version with Bumblefoot is out there it would not be the first time a song has leaked after his guitar has been added to it. If BBF’s version was intercepted then it is possible that like  Going Down, Silkworms and OMG before it the song is panned into the right ear while his overdubs are  mixed to the left.

Among the versions of Atlas Shrugged that leaked in September of 2019 are the mix labelled 3/27/00 from rough mixes CD#1, one of the many Cd’s taken from what became known as the Locker leaks. This version contains Josh Freese on drums with sparse rhythm compared to the other version, the line “In fact” seems punched in and the song as a whole feels less complete. This seems to be the earliest version of the song with Brian May on as this mix is from only three months after he recorded his guitar for it.
The next version also from the locker leaks comes from the CD labeled J587 219 and has Brain on drums. The song feels heavier and far more complete than the previous version. There are three versions on the CD however they are almost no differences between them, at least to my ears.

The 3 tracks on the disk are the song with drums at a regular level and then versions with the drums lowered and raised by 1.5 Db.
A version of the song was in the hands of some hoarders as of 2007 however this version has not leaked. A version comparable to the 2019 leaks were in the hands of some around 2015/16.

If this is wrong blame gemini not me...

Physical Versions (Pre-order Information)
The official pre-orders for the physical versions of the "Nothin' / Atlas" single are set to begin on December 12, 2025.

You can use the official link hub below, which currently directs to streaming/digital platforms but will likely be updated with the store links once the pre-orders go live:

Official Singles Link Hub https://gunsnroses.lnk.to/nothinatlas

The physical formats available will include:

7-inch vinyl

Guns N' Roses store-exclusive cassette

Japan-exclusive SHM-CD

I'd imagine your Dominguez interview annoyed them a little. Given what Dizzy said about the song I'm assuming the clip you were sent had Izzy on vocals and not Axl? If it had any vocals of course.

Yeah I like Nothing too, probably the best of the post CD songs to be fair

'On a restless sea' = Down by the ocean/Down by the sea? probably not but who knows. I remember Axl saying Fink played an SRV style solo on one song, I would imagine that was Nothing.