Fantastic list! I always had a feeling that Wikipedia was wrong, and that the 80s syndicated episodes I had were actually correct. I saw a CBS network copy of #21 ages ago, and it matches up perfectly to your list!
I also have 9 episodes on DVD from the 80s (aired on a FOX syndicate I think FOX-25), some 80s syndicated episodes in horrid quality/incomplete, nd a handful of episodes from Nickelodeon (which only have 1 musical segment, instead of 2). I ALSO have a lot of single segments, so any episodes marked as (components) means I have all the bits from that episode, but separated. So, I have:
#1 (2015 DVD)
#2 (FOX)
#3 (Nick; The Magic Mountain is cut, a segment I lack from my Alvin Show collection in any form)
#4 (2015 DVD)
#5 (Nick; The Little Dog is cut, which I only have in a shortened, sing-along form)
#6 (FOX)
#7 (Nick; The Pidgin English Hula is cut, a segment I lack from my Alvin Show collection in any form)
#8 (Nick; Stuck in Arabia is cut, a segment I lack from my Alvin Show collection in any form)
#9 (FOX)
#10 (2015 DVD)
#11 (Nick; Alvin for President is cut, but I have that segment; First Aid is missing around 20 - 30 seconds)
#12 (FOX)
#13 (FOX)
#14 (FOX)
#15 (FOX; SUPER BAD QUALITY, but I have all of it minus Clyde in better quality)
#17 (FOX)
#19 (FOX; REALLY BAD QUALITY; can't remember if this one is incomplete or not)
#20 (FOX)
#22 (components... sorta; The Band Played On is a shortened, sing-along version)
There's also some episodes I have in components, OTHER THAN CLYDE; those are..
#18
#19
#21 (Whistle While You Work is in black and white)
#23
I do have some other segments, but this is most of what I have. If allowed, I'll share what I have, as soon as I get a new computer. Hopefully, SOMEONE has some stuff I don't and perhaps, one day, either by Badgasarian or the fans, will have the entire series.