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Fixed - Fortunately I had the correct version still sitting in a file on my disk after two years! Must of just mis-pasted during one of the edits. This version is still 138 characters.
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Haskell - 147 142 138 characters

fi=zz.bu
bu=zz.(:).(++"zz")
[]#zz=zz;zz#__=zz
zZ%zz=zZ zz$zZ%zz
zz=(([[],[]]++).)
zZ=zipWith;z=zZz=zipWith3(((#).show)[1..]$zZ(++))(bu%"Fi")(fi%"Bu")$map show[1..]

The code is 19 characters longer than it needs to be, but I thought the aesthetics were worth it! I believe all three "objectives" are satisfied.

> take 20 z
["1","2","Fizz","4","Buzz","Fizz","7","8","Fizz","Buzz","11","Fizz","13","14",
"FizzBuzz","16","17","Fizz","19","Buzz"]

Haskell - 147 142 138 characters

fi=zz.bu
bu=zz.(:).(++"zz")
[]#zz=zz;zz#__=zz
zZ%zz=zZ zz$zZ%zz
zz=(([[],[]]++).)
zZ=zipWith;z=zZ((#).show)[1..]$zZ(++)(bu%"Fi")(fi%"Bu")

The code is 19 characters longer than it needs to be, but I thought the aesthetics were worth it! I believe all three "objectives" are satisfied.

> take 20 z
["1","2","Fizz","4","Buzz","Fizz","7","8","Fizz","Buzz","11","Fizz","13","14",
"FizzBuzz","16","17","Fizz","19","Buzz"]

Haskell - 147 142 138 characters

fi=zz.bu
bu=zz.(:).(++"zz")
[]#zz=zz;zz#__=zz
zZ%zz=zZ zz$zZ%zz
zz=(([[],[]]++).)
z=zipWith3(((#).).(++))(bu%"Fi")(fi%"Bu")$map show[1..]

The code is 19 characters longer than it needs to be, but I thought the aesthetics were worth it! I believe all three "objectives" are satisfied.

> take 20 z
["1","2","Fizz","4","Buzz","Fizz","7","8","Fizz","Buzz","11","Fizz","13","14",
"FizzBuzz","16","17","Fizz","19","Buzz"]
deleted 1 characters in body
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Haskell - 147 142 138 characters

fi=zz.bu
bu=zz.(:).(++"zz")
[]#zz=zz;zz#__=zz
zZ%zz=zZ zz$zZ%zz
zz=(([[],[]]++).)
z=zipWith3(zZ=zipWith;z=zZ((#).show)[1..]$zZ(++))(bu%"Fi")(fi%"Bu")$map show[1..]

The code is 19 characters longer than it needs to be, but I thought the aesthetics were worth it! I believe all three "objectives" are satisfied.

> take 20 aaz
["1","2","Fizz","4","Buzz","Fizz","7","8","Fizz","Buzz","11","Fizz","13","14",
"FizzBuzz","16","17","Fizz","19","Buzz"]

Haskell - 147 142 138 characters

fi=zz.bu
bu=zz.(:).(++"zz")
[]#zz=zz;zz#__=zz
zZ%zz=zZ zz$zZ%zz
zz=(([[],[]]++).)
z=zipWith3(((#).).(++))(bu%"Fi")(fi%"Bu")$map show[1..]

The code is 19 characters longer than it needs to be, but I thought the aesthetics were worth it! I believe all three "objectives" are satisfied.

> take 20 aa
["1","2","Fizz","4","Buzz","Fizz","7","8","Fizz","Buzz","11","Fizz","13","14",
"FizzBuzz","16","17","Fizz","19","Buzz"]

Haskell - 147 142 138 characters

fi=zz.bu
bu=zz.(:).(++"zz")
[]#zz=zz;zz#__=zz
zZ%zz=zZ zz$zZ%zz
zz=(([[],[]]++).)
zZ=zipWith;z=zZ((#).show)[1..]$zZ(++)(bu%"Fi")(fi%"Bu")

The code is 19 characters longer than it needs to be, but I thought the aesthetics were worth it! I believe all three "objectives" are satisfied.

> take 20 z
["1","2","Fizz","4","Buzz","Fizz","7","8","Fizz","Buzz","11","Fizz","13","14",
"FizzBuzz","16","17","Fizz","19","Buzz"]
now with more zz
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Haskell - 147 142142 138 characters

[]#aa=aa
aa#__=aa
zz=((([]:).([]:))fi=zz.)bu
bu=zz.(:).(++"zz")
fi=zz.bu[]#zz=zz;zz#__=zz
aa%zz=aazZ%zz=zZ zzzz$zZ%zz
zz=(aa%zz([[],[]]++).)
aa=zipWith3z=zipWith3(((#).).(++))(bu%"Fi")(fi%"Bu")$map show[1..]

The code is 19 characters longer than it needs to be, but I thought the aesthetics were worth it! I believe all three "objectives" are satisfied.

> take 20 aa
["1","2","Fizz","4","Buzz","Fizz","7","8","Fizz","Buzz","11","Fizz","13","14",
"FizzBuzz","16","17","Fizz","19","Buzz"]

Haskell - 147 142 characters

[]#aa=aa
aa#__=aa
zz=((([]:).([]:)).)
bu=zz.(:).(++"zz")
fi=zz.bu
aa%zz=aa zz(aa%zz)
aa=zipWith3(((#).).(++))(bu%"Fi")(fi%"Bu")$map show[1..]

The code is 19 characters longer than it needs to be, but I thought the aesthetics were worth it! I believe all three "objectives" are satisfied.

> take 20 aa
["1","2","Fizz","4","Buzz","Fizz","7","8","Fizz","Buzz","11","Fizz","13","14",
"FizzBuzz","16","17","Fizz","19","Buzz"]

Haskell - 147 142 138 characters

fi=zz.bu
bu=zz.(:).(++"zz")
[]#zz=zz;zz#__=zz
zZ%zz=zZ zz$zZ%zz
zz=(([[],[]]++).)
z=zipWith3(((#).).(++))(bu%"Fi")(fi%"Bu")$map show[1..]

The code is 19 characters longer than it needs to be, but I thought the aesthetics were worth it! I believe all three "objectives" are satisfied.

> take 20 aa
["1","2","Fizz","4","Buzz","Fizz","7","8","Fizz","Buzz","11","Fizz","13","14",
"FizzBuzz","16","17","Fizz","19","Buzz"]
shorter, better objectives met!
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slight renaming
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