I think my pre-1990 list for the first three rounds is complete. This is what it will almost certainly look like, and I found it really interesting seeing some bands on there that I just can't square with the 80s, but which did release their first albums towards the end of that decade.
Pre-1990 completely banned:
Alannah Myles
Bad Religion
The Beatles
Blind Guardian
Chick Corea & Return to Forever
Chris Squire
Dream Theater
Extreme
Fates Warning
Guns n' Roses
Helloween
Iron Maiden
Jane's Addiction
Jeff Wayne
King Crimson
Living Colour
Loreena McKennitt
Megadeth
Metallica
Nirvana
The Offspring
Pink Floyd
Queen
Queensryche
Red Hot Chili Peppers
Rush
Sarah McLachlan
Yngwie Malmsteen
Pre-1990 partially banned:
The Alan Parsons Project - everything up to and including Ammonia Avenue (1976-84); Gaudi (1987)
Andrew Lloyd Webber & Tim Rice - Jesus Christ Superstar (1970)
Area - Crac! (1975); 1978 gli dei se ne vanno, gli arrabbiati restano! (1978)
Asia - Asia (1982)
Average White Band - AWB (1974); Cut the Cake (1975)
Bill Evans - Symbiosis (1974)
Billy Joel - Turnstiles (1976); Storm Front (1989)
Birth Control - Operation (1971)
Black Sabbath - everything up to and including Sabbath Bloody Sabbath (1970-73); Heaven and Hell (1980); Mob Rules (1981)
Bob Dylan - Highway 61 Revisited (1965); Bringing It All Back Home (1965); Blonde on Blonde (1966)
Buddy Rich - Big Swing Face (1967)
Can - Tago Mago (1971); Landed (1975)
Cardiacs - A Little Man and a House and the Whole World Window (1988); On Land and in the Sea (1989)
Casiopea - Euphony (1988)
Charles Mingus - Mingus Ah Um (1959); Blues & Roots (1960); The Black Saint and the Sinner Lady (1963)
Charlie Parker - The Genius of Charlie Parker (1955)
Cheap Trick - Dream Police (1979)
Cowboy Junkies - The Trinity Session (1988)
Crack the Sky - Crack the Sky (1975)
Crimson Glory - Transcendence (1988)
Crosby, Stills & Nash - Crosby, Stills & Nash (1969)
The Cult - Sonic Temple (1989)
The Cure - Disintegration (1989)
David Bowie - The Rise and Fall of Ziggy Stardust and the Spiders From Mars (1972)
Deep Purple - Machine Head (1972); Made in Japan (1972); Perfect Strangers (1984)
Depeche Mode - Some Great Reward (1984); Black Celebration (1986); Music for the Masses (1987)
Dio - Holy Diver (1983); The Last in Line (1984)
Dire Straits - Making Movies (1980); Love Over Gold (1982); Brothers in Arms (1985)
Diz and Getz - Diz and Getz (1955)
Dizzy Gillespie - Have Trumpet, Will Excite! (1959); Perceptions (1961)
Eagles - Hotel California (1976)
Emerson, Lake & Palmer - Tarkus (1971); Pictures at an Exhibition (1972); Trilogy (1972)
Eric Clapton - Journeyman (1989)
Faith No More - The Real Thing (1989)
Fields of the Nephilim - The Nephilim (1988)
Funkadelic - Maggot Brain (1971); Standing on the Verge of Getting It On (1974)
Genesis - everything from Trespass to The Lamb Lies Down on Broadway (1970-74); Wind & Wuthering (1976)
Gentle Giant - Acquiring the Taste (1971); Free Hand (1975)
George Harrison - Cloud Nine (1987)
Gino Vannelli - Storm at Sunup (1975); A Pauper in Paradise (1977); Brother to Brother (1978)
Gowan - Strange Animal (1985)
Herbie Hancock - Takin' Off (1962)
Iggy Pop - Lust for Life (1977)
Jaco Pastorius - Invitation (1983)
Jethro Tull - Aqualung (1971); The Broadsword and the Beast (1982)
Jimi Hendrix - Are You Experienced (1967); Axis: Bold as Love (1967)
John Coltrane - Blue Train (1958); Soultrane (1958); Giant Steps (1960); Standard Coltrane (1962); A Love Supreme (1965)
Joy Division - Closer (1980)
Kansas - Masque (1975); Leftoverture (1976); Point of Know Return (1977)
Led Zeppelin - Led Zeppelin II (1969); Led Zeppelin [IV] (1971); Physical Graffiti (1975)
Lizzy Borden - Master of Disguise (1989)
Lucifer's Friend - Banquet (1974); Mind Exploding (1976); Good Time Warrior (1978)
Madness - any tracks on the Divine Madness compilation
The Mahavishnu Orchestra With John McLaughlin - The Inner Mounting Flame (1971)
Marillion - Script for a Jester's Tear (1983); Misplaced Childhood (1985); first half-ish of Clutching at Straws (1987)
Maynard Ferguson - Chameleon (1974); Hollywood (1982); any tracks on the This is Jazz 16 compilation
Meat Loaf - Bat Out of Hell (1977); any songs on the Hits Out of Hell compilation
Michael Jackson - Thriller (1982); Bad (1987); any songs later included on the History best of disc
The Michael Schenker Group - The Michael Schenker Group (1980)
Michel Camilo - Michel Camilo (1988)
Miles Davis - Kind of Blue (1959); Sketches of Spain (1960); Bitches Brew (1970); Aura (1989)
NEU! - NEU! (1972); NEU! 2 (1973)
Oscar Peterson Trio - Night Train (1963); Oscar Peterson Trio + One, Clark Terry (1964)
Ozzy Osbourne - Diary of a Madman (1981)
Parliament - Up for the Down Stroke (1974); Mothership Connection (1975); The Clones of Dr. Funkenstein (1976); Funkentelechy vs. the Placebo Syndrome (1977)
Pixies - Surfer Rosa (1988); Doolittle (1989)
R.E.M. - Lifes Rich Pageant (1986); Document (1987)
Rainbow - everything up to and including Down to Earth (1975-79)
Randy Newman - Land of Dreams (1988)
Run-D.M.C. - Raising Hell (1986)
Scott Walker - Climate of Hunter (1984)
Simon & Garfunkel - any tracks from the 20 Greatest Hits compilation
Stan Getz & Joao Gilberto - Getz / Gilberto (1964)
Steely Dan - Aja (1977)
Stephen Sondheim - Into the Woods [Original Cast Recording] (1988)
Stevie Wonder - Talking Book (1972); Innervisions (1973); Fulfillingness' First Finale (1974); Songs in the Key of Life (1976)
Sting - ...Nothing Like the Sun (1987)
Talk Talk - It's My Life (1984); The Colour of Spring (1986); Spirit of Eden (1988)
Tom Waits - everything up to and including Blue Valentine (1973-78); Rain Dogs (1985)
Toto - Toto (1978); IV (1982); Isolation (1984); Fahrenheit (1986); The Seventh One (1988)
Tower of Power - Bump City (1972); In the Slot (1975); Ain't Nothin' Stoppin' Us Now (1976); Direct (1981)
UFO - Lights Out (1977)
Van der Graaf Generator - Pawn Hearts (1971)
The Velvet Underground & Nico - The Velvet Underground & Nico (1967)
Virgin Steele - Noble Savage (1985); Age of Consent (1988)
Wes Montgomery - Bumpin' (1965)
The Who - Tommy (1969); Who's Next (1971); Quadrophenia (1973)
Wishbone Ash - everything up to and including There's the Rub (1970-74); New England (1976)
Yes - everything up to and including 90125 (1969-83)