Jeff did start working on it initially when they were working on Free as a Bird and Real Love, but apparently they did very little work on it. But you're right - Jeff did have some involvement.
Jeff was of course the lead producer for the original attempt to work on the track, but couldn't get around John's muffled voice or the TV playing in the background. It just wasn't a usable track at the time. This time around, though, Paul went straight to Peter Jackson's team. I don't think Jeff's name even came up for this round of work.
I think the Wilbury feel in the finished tracks is from the especially strummy sound of George's acoustic guitar from the Anthology-vintage session. If you watch the videos from around that time, including the excerpts in the 12-minute Now and Then short video linked elsewhere on this thread, all you see is George playing acoustic. (And ukulele of course!) That's just where he was in the late 90s.
So while Jeff had ZERO involvement in THIS round of production on Now and Then, his recording of George's acoustic guitar is nevertheless the bedrock of the finished version, the one element running throughout every measure of the song.
We can argue about whether that guitar sound was George or Jeff -- George really was playing very nearly only acoustic in those days, and had of course done so to great effect going back to My Sweet Lord, and before that to And I Love Her, where Paul acknowledged that George's acoustic lick was the best part of the song -- but that almost choral, nay, orchestral sound of an acoustic guitar has been core part of Jeff's sound since the mid-70s.
You can hear it on the Electric Light Orchestra track "Living Thing" in particular, but you can hear it on other Jeff productions, too, of course. Most notable to me are Tom Petty's "Learning To Fly", but also on all of George Harrison's Cloud Nine album, especially "Got My Mind Set on You", but especially on the George-driven Wilburys track, "Handle With Care", where all five singers played acoustic guitar (!!!), with George's nifty slide solo, and Jeff adding some electric guitars when he and George finished the album at Friar Park.
Jeff's integration into the Beatleverse always made a lot of sense to me. John was a fan of ELO, and whenever anybody bothered him about a Beatles reunion in the early-to-mid-70s, he pointed them to ELO, in a positive way. They clearly had roots in The Beatles, specifically, the riff-based rock-and-roll of "I Am The Walrus", where the lead instrument was the orchestra, rather than, say, the strings on Eleanor Rigby, which led to a whole subgenre of baroque pop. ELO was anything but baroque! Rococo if anything, but they really did lean to the more classical (in the "era" sense of classical) sound of Walrus.
There's a fantastic guitar outro to that track of course, but otherwise, every riff you can hum in Walrus is made by an orchestra! John's point was, why ask me to go backward, when there are people like Jeff Lynne who took The Beatles sound and were moving it forward! Listen to ELO's "Can't Get It Out of My Head", followed by John's "#9 Dream" and you can hear just how closely John was not just
listening to Jeff, but
studying him, and learning from him. I don't doubt for a second that John would have approved of Jeff as the producer for a new collaboration with these four fellows. He may very well have
suggested it, given the opportunity.
In addition to George, Jeff also worked with Ringo and Paul McCartney, producing 8 of the tracks on 1997's Flaming Pie, as well as one of the b-sides.
Paul really liked Jeff's sound, as well as his work on the Anthology, but asked Jeff to dial it back a bit. He felt that they'd get more mileage out of Jeff's approach if they intentionally subverted it a bit, and Jeff was game. A lot of the album is just him and Paul, recorded much more quickly than Jeff typically worked, and it was indeed a lovely, more balanced approach than Jeff's productions sometimes have. I love Jeff's work in ELO and beyond (and in The Move before ELO), but agree with Paul that his handiwork can be a lot.
So to my ears, I'm not hearing the Wilburys per se, and I think if you listen to the Jeff-produced Free As A Bird and Real Love alongside Now and Then, you'll hear that the overall productions are really not much alike at all, and even somebody who's never heard ELO or the Wilburys will immediately be able to tell which tracks were produced by one guy and which one was produced by someone else....but that underlying acoustic track of George's? Well, that has Jeff's fingerprints on it, no doubt about that.
I do love this particular angle on the conversation, so I'm going to add some documentation.
I've been meaning to start a thread on the new-ish channel started by Burt Sugarman for The Midnight Special, and I will, but here's a dandy 1977 version of Livin' Thing. ELO really were terrific live. In addition to Jeff's super-duper-strummy acoustic guitar, note his lack of sunglasses! I think this episode of The Midnight Special was the last time we saw his naked eyes! Note also a TON of augmented chords, a trick he happily acknowledged at the time as lifting from George Harrison!
Tom Petty, Learning to Fly, 1991. Man, I love this! Most of the time you ask me, this is my favorite Tom Petty song, even if a few others ocassionally elbow their way to the top of the list...but wow, those strummy guitars!!!
George famously came to the US before his bandmates, on a trip to visit his sister Louise, who'd married an American. He bought a Rickenbacker guitar on that trip (!!!), as well as a bunch of records, including an album from James Ray, who had a terrific song on the charts that George tucked away for later.
You've already heard George's cover, so need to include that here. Jeff obviously knew how to manage an R&B cover, as ELO's first US hit was a cover of Roll Over Beethoven with some especially cheeky Beethoven musical quotes, originally from the 9th Symphony tacked on to the end of live performances, but later using the opening "riff" from the 5th Symphony as the opening riff to their cover, and repeated a couple of times throughout. George's cover of Got My Mind Set On You is lush by George's standards, but still stripped down from the original, but certainly counts as another classically-flavored R&B success for Jeff as a producer-arranger.
That said, this is the perfect time to bring up George's When We Was Fab, a song he cowrote with Jeff. In addition to some adorable appearances by Ringo, who plays drums on the track, note the orchestral bits, George's super-strummy acoustic in the background (although George is only seen playing electric in the video). There's also, appropriately enough, lots of cello and other orchestral stylings, as well as some sitar. All the bases are touched!
There are cameos in the video from Jeff Lynne (who played bass on the track) and Elton John, and while Paul had hoped to participate, he couldn't make it. He suggested that George use a walrus-masked bassist in the video and TELL people it was Paul, which George indeed did for years. The video's directors, Kevin Godley and Lol Creme (from the band 10cc, but who later had a terrific later career as
video directors) later 'fessed up....but their video here in 1988 long predates a past-present pastiche approach that Jackson took more clumsily artistically, if far more technically precisely, for Now and Then. This really is a gas, and nicely ties all of this together.
I should also note that the conversation with Paul about Jeff Lynne is from an especially unlikely source -- Alice Cooper! We all know that Alice is a more thoughtful fellow than his public persona suggests, especially in his sobriety, but he's got a dandy podcast with lots of terrific guests.
Here's a link to some text highlights from the interview with Paul. You'll find on the same page a link to the podcast itself in the right sidebar.