There's definitely only one recording of the "Recurring Dream" instrumental parts. Every version is some variation of the original recording. Either an edit to add in the second verse, new vocals, or different mixes. The band went into the studio one time (I assume in 1985) to lay down the track. Everything afterwards has been Neil or maybe Mitchell messing with it? Here are the liner notes from the versions I have seen:
Rikky and Pete (Original Soundtrack)
1988
Recurring Dream (Finn - Hester - Seymour - Hooper) 2:52
Produced by Eddie Rayner and Neil Finn
Courtesy of Capitol Records Inc. Special Markets
Tequila Sunrise (Original Soundtrack)
1988
Recurring Dream (Neil Finn)
Produced by Mitchell Froom
Mixed by Michael Fronelli
Four Seasons In One Day (UK single)
1992
Recurring Dream (Finn/Seymour/Hester/Hooper) 3:25
Produced by Mitchell Froom
(c) 1988 Capitol Records Inc.
Afterglow
1999
Recurring Dream (Neil Finn / Paul Hester / Nick Seymour / Craig Hooper) 3:25
Produced by Crowded House
Recorded at Platinum Studios 1985
Mixed by Michael Fronelli
Crowded House (deluxe version)
2016
Recurring Dream (original version) 2:52
-no song writing credits-
Produced by Eddie Rayner at Platinum Studios, Melbourne 1986
Originally released in 1986 as the B-side to "Now We're Getting Somewhere" in Australia and then on the "Rikki and Pete" soundtrack in 1988. Later overdubbed for the "Tequila Sunrise" soundtrack and included on Afterglow.
--So, it was either produced by Eddie Rayner, Eddie and Neil, Mitchell Froom or Crowded House in 1985 or 1986 and then overdubbed "later" presumably in 1988 for inclusion on the Tequila Sunrise soundtrack, which I do not have but I found a photo of the liner notes on Amazon.
I think there are only two versions: the original short version, the second longer overdubbed version (with the same instrumental track) and then potentially new mixes of those two versions for inclusion on Afterglow and the deluxe version of Crowded House.