All Simpsons episodes from Season 1 originally had the "flying 'Television text" logo at the end, meaning the other logos were changed. Therefore the episodes aren't truly uncut and I don't see why they did this: there's no need to put the new logos on video, it's bad enough they do this on TV.
I believe this is the history of logos on "The Simpsons:
Seasons 1-3: aforementioned 1988 20th Century Fox Television logo with flying text and shortened movie fanfare music
Season 4 (and maybe later season 3 eps?): early 20th Television logo without News Corp. byline (same music)
Season 5-7: 20th Television logo with News Corporation byline (same music again)
Season 8-present: 20th Century Fox Television current logo (same logo as 20th Television but different company name). Initially the '88 music was used. then during season 9 the music was changed to a remake of the Fox TV theme from the '60s and '70s (this may be the music you are referring to as the "heavily synthesized kazoo anthem" but it is orchestral, no synths OR kazoos.) Also, when Fox started putting generic credits on the show, they put their own network jingle (the drumroll from the full-length fanfare) with the logo, but when the regular credits are shown you hear the '60s/'70s fanfare remake.
In syndication all eps from seasons 1-7 have the 20th Television/News Corp logo with 1988 music, season 8 has 20th Century Fox Television w/ '88 music, season 9 has 20th Television/News Corp. with reorchestrated '88 music, and seasons 10-present have the current 20th Century Fox TV logo.
By the way, the Closing Logo Group is still alive! It was deleted by some hacker from the game show newsgroup, but there are two new homes for it (it hasn't really been decided what the official group is): http://groups.yahoo.com/group/closinglogogroup
and
http://groups.yahoo.com/group/closinglogo
Eric Hartman's website is also still here the URL is: http://www.angelfire.com/tv2/closinglogo/
Join us!